BIVARIATE SUPPORT OF FORWARD LIBOR AND SWAP RATES

Based on a certain notion of "prolific process," we find an explicit expression for the bivariate (topological) support of the solution to a particular class of 2 × 2 stochastic differential equations that includes those of the three-period "lognormal" Libor and swap market models. This yields that in the lognormal swap market model (SMM), the support of the 1 × 1 forward Libor   L * _t   equals  [ l * _t , ∞)  for some semi-explicit  −1 ≤ l * _t ≤ 0  , sharpening a result of Davis and Mataix-Pastor (2007) that forward Libor rates (eventually) become negative with positive probability in the lognormal SMM. We classify the instances   l * _t < 0  , and explicitly calculate the threshold time at or before which   L * _t   remains positive a.s.     

INTENSITY-BASED VALUATION OF RESIDENTIAL MORTGAGES: AN ANALYTICALLY TRACTABLE MODEL

This paper presents an analytically tractable valuation model for residential mortgages. The random mortgage prepayment time is assumed to have an intensity process of the form h _t = h ₀( t ) +γ ( k − r _t )⁺ , where h ₀( t ) is a deterministic function of time, r _t is the short rate, and γ and k are scalar parameters. The first term models exogenous prepayment independent of interest rates (e.g., a multiple of the PSA prepayment function). The second term models refinancing due to declining interest rates and is proportional to the positive part of the distance between a constant threshold level and the current short rate. When the short rate follows a CIR diffusion, we are able to solve the model analytically and find explicit expressions for the present value of the mortgage contract, its principal-only and interest-only parts, as well as their deltas. Mortgage rates at origination are found by solving a non-linear equation. Our solution method is based on explicitly constructing an eigenfunction expansion of the pricing semigroup, a Feynman-Kac semigroup of the CIR diffusion killed at an additive functional that is a linear combination of the integral of the CIR process and an area below a constant threshold and above the process sample path (the so-called area functional). A sensitivity analysis of the term structure of mortgage rates and calibration of the model to market data are presented.     

MARTINGALE MEASURES FOR DISCRETE-TIME PROCESSES WITH INFINITE HORIZON

Let ( S_t ) _tεI be an R^d-valued adapted stochastic process on (Ω, , ( _t ) _tεI , P ). A basic problem occurring notably in the analysis of securities markets, is to decide whether there is a probability measure Q on  equivalent to P such that ( S_t ) _tεI is a martingale with respect to Q. It is known (see the fundamental papers of Harrison and Kreps 1979; Harrison and Pliska 1981; and Kreps 1981) that there is an intimate relation of this problem with the notions of "no arbitrage" and "no free lunch" in financial economics. We introduce the intermediate concept of "no free lunch with bounded risk." This is a somewhat more precise version of the notion of "no free lunch." It requires an absolute bound of the maximal loss occurring in the trading strategies considered in the definition of "no free lunch." We give an argument as to why the condition of "no free lunch with bounded risk" should be satisfied by a reasonable model of the price process ( S_t ) _tεI of a securities market. We can establish the equivalence of the condition of "no free lunch with bounded risk" with the existence of an equivalent martingale measure in the case when the index set I is discrete but (possibly) infinite. A similar theorem was recently obtained by Delbaen (1992) for continuous-time processes with continuous paths. We can combine these two theorems to get a similar result for the continuous-time case when the process ( S_t ) _{t εR+} is bounded and, roughly speaking, the jumps occur at predictable times. In the infinite horizon setting, the price process has to be "almost a martingale" in order to allow an equivalent martingale measure.     

The Fundamental Theorem of Asset Pricing under Proportional Transaction Costs in Finite Discrete Time

We prove a version of the Fundamental Theorem of Asset Pricing, which applies to Kabanov's modeling of foreign exchange markets under transaction costs. The financial market is described by a   d × d   matrix-valued stochastic process  (Π _t ) ^T _{t =0}  specifying the mutual bid and ask prices between d assets. We introduce the notion of "robust no arbitrage," which is a version of the no-arbitrage concept, robust with respect to small changes of the bid-ask spreads of  (Π _t ) ^T _{t =0}  . The main theorem states that the bid-ask process  (Π _t ) ^T _{t =0}  satisfies the robust no-arbitrage condition iff it admits a strictly consistent pricing system. This result extends the theorems of Harrison-Pliska and Kabanov-Stricker pertaining to the case of finite Ω, as well as the theorem of Dalang, Morton, and Willinger and Kabanov, Rásonyi, and Stricker, pertaining to the case of general Ω. An example of a  5 × 5  -dimensional process  (Π _t )² _{t =0}  shows that, in this theorem, the robust no-arbitrage condition cannot be replaced by the so-called strict no-arbitrage condition, thus answering negatively a question raised by Kabanov, Rásonyi, and Stricker.     

Analysis of Error with Malliavin Calculus: Application to Hedging

The aim of this paper is to compute the quadratic error of a discrete time-hedging strategy in a complete multidimensional model. This result extends that of Gobet and Temam (2001) and Zhang (1999) . More precisely, our basic assumption is that the asset prices satisfy the d -dimensional stochastic differential equation   dXⁱ_t = Xⁱ_t ( bⁱ ( X_t ) dt +σ _{i , j} ( X_t ) dW^j_t )  . We precisely describe the risk of this strategy with respect to n , the number of rebalancing times. The rates of convergence obtained are     for any options with Lipschitz payoff and  1/ n ^1/4  for options with irregular payoff.     

OPTIMAL INVESTMENT STRATEGIES FOR CONTROLLING DRAWDOWNS

We analyze the optimal risky investment policy for an investor who, at each point in time, wants to lose no more than a fixed percentage of the maximum value his wealth has achieved up to that time. In particular, if M _t is the maximum level of wealth W attained on or before time t , then the constraint imposed on his portfolio choice is that W_tα M _t, where α is an exogenous number betweenα O and 1. We show that, for constant relative risk aversion utility functions, the optimal policy involves an investment in risky assets at time t in proportion to the "surplus" W _t - α M _t. the optimal policy may appear similar to the constant-proportion portfolio insurance policy analyzed in Black and Perold (1987) and Grossman and Vila (1989). However, in those papers, the investor keeps his wealth above a nonstochastic floor F instead of a stochastic floor α M _t. the stochastic character of the floor studied here has interesting effects on the investment policy in states of nature when wealth is at an all-time high; i.e., when Wt = M _t. It can be shown that at W _t= M _t, α M _t is expected to grow at a faster rate than W _t, and therefore the investment in the risky asset can be expected to fall. We also show that the investment in the risky asset can be expected to rise when W _t is close to α M _t. We conjecture that in an equilibrium model the stochastic character of the floor creates "resistance" levels as the market approaches an all-time high (because of the reluctance of investors to take more risk when W _t= M _t).     

Asymptotics of the price oscillations of a European call option in a tree model

It is well known that the price of a European vanilla option computed in a binomial tree model converges toward the Black-Scholes price when the time step tends to zero. Moreover, it has been observed that this convergence is of order 1/ n in usual models and that it is oscillatory. In this paper, we compute this oscillatory behavior using asymptotics of Laplace integrals, giving explicitly the first terms of the asymptotics. This allows us to show that there is no asymptotic expansion in the usual sense, but that the rate of convergence is indeed of order 1/ n in the case of usual binomial models since the second term (in     ) vanishes. The next term is of type   C ₂( n )/ n   , with   C ₂( n )  some explicit bounded function of n that has no limit when n tends to infinity.     

Leland's Approach to Option Pricing: The Evolution of a Discontinuity

A claim of Leland (1985) states that in the presence of transaction costs a call option on a stock S , described by geometric Brownian motion, can be perfectly hedged using Black–Scholes delta hedging with a modified volatility. Recently Kabanov and Safarian (1997) disproved this claim, giving an explicit (up to an integral) expression of the limiting hedging error, which appears to be strictly negative and depends on the path of the stock price only via the stock price at expiry S _T . We prove in this paper that the limiting hedging error, considered as a function of S _T , exhibits a removable discontinuity at the exercise price. Furthermore, we provide a quantitative result describing the evolution of the discontinuity: Hedging errors, plotted over the price at expiry, show a peak near the exercise price. We determine the rate at which that peak becomes narrower (producing the discontinuity in the limit) as the lengths of the revision intervals shrink.     

A Counterexample to Several Problems In the Theory of Asset Pricing

We construct a continuous bounded stochastic process ( S _t,) _1E[0,1] which admits an equivalent martingale measure but such that the minimal martingale measure in the sense of Föllmer and Schweizer does not exist. This example also answers (negatively) a problem posed by Karatzas, Lehozcky, and Shreve as well as a problem posed by Strieker.     

The US stock market and the international value of the US dollar

We investigate the spillover effect of the US equity market on the value of the dollar and therefore on the return and volatility of US equity investments for the international investor. The data are daily observations of the S & P 500 and the US dollar in terms of seven foreign currencies covering the period 1971–2002. Using Geweke measures of feedback, we find a high percentage of contemporaneous association between daily movements in the S & P 500 index and changes in the value of the dollar. A consistently positive relationship between the S & P 500 and the dollar is found for the period 1992–2002, creating a compounding effect for the foreign investor in US equities. However, investment by foreigners in US equities did not result in consistently higher returns but in higher volatility compared to their US counterparts for the period 1971–2002.     

Deal Structuring in Philanthropic Venture Capital Investments: Financing Instrument,Valuation and Covenants

Philanthropic venture capital (PhVC) is a financing option available for social enterprises that, like traditional venture capital, provides capital and value-added services to portfolio organizations. Differently from venture capital, PhVC has an ethical dimension as it aims at maximizing the social return on the investment. This article examines the deal structuring phase of PhVC investments in terms of instrument used (from equity to grant), valuation, and covenants included in the contractual agreement. By content analyzing a set of semi-structured interviews and thereafter surveying the entire population of PhVC funds that are active in Europe and in the United States, findings indicate that the non-distribution constraint holding for non-profit social enterprises is an effective tool to align the interests of both investor and investee. This makes the investor behaving as a steward rather than as a principal. Conversely, while backing non-profit social ventures, philanthropic venture capitalists structure their deal similarly as traditional venture capital, as the absence of the non-distribution constraint makes such investments subject to moral hazard risk both in terms of perks and stealing and social impact focus.     

A COUNTEREXAMPLE CONCERNING THE VARIANCE-OPTIMAL MARTINGALE MEASURE

The present note addresses an open question concerning a sufficient characterization of the variance-optimal martingale measure. Denote by S the discounted price process of an asset and suppose that   Q ^★  is an equivalent martingale measure whose density is a multiple of  1 −φ· S _T   for some S -integrable process φ. We show that   Q ^★  does not necessarily coincide with the variance-optimal martingale measure, not even if  φ· S   is a uniformly integrable   Q ^★  -martingale.     

How venture capital firms differ

Four potential sources of differences between venture capital (VC) firms were examined—venture stage of interest, amount of assistance provided by the VC, VC firm size, and geographic region where located. Through a questionnaire, 149 venture capitalists provided data about their firms, about what they look for in evaluating an investment, and about how they work with a portfolio company following an investment.Firms were divided into four groups based on venture stage of interest. The earlier the investment stage, the greater the interest in potential investments built upon proprietary products, product uniqueness, and high growth markets. Late-stage investors were more interested in demonstrated market acceptance.There were no differences by stage regarding the desired qualities of management. However, after the investment was made, earlier stage investors attached more importance to spending their time evaluating and recruiting managers. Earlier stage investors sought ventures with higher potential returns—a 42% hurdle rate of return for the earliest stage investor versus 33% for the late-stage investor.Late-stage investors spent more time evaluating a potential investment. However, after the investment was made, there was little difference in the amount of time spent assisting the portfolio company. There were, however, differences in the significance that VCs attached to particular post-investment activities. Firms were split into three groups based upon the amount of time the VC spent with a portfolio company after an investment was made as lead investor. The most active group averaged over 35 hours per month per investment, and the least active group averaged less than seven hours.The difference in assistance provided was not strongly tied to differences in investment stage of interest. There were major differences in the importance the VCs attached to their post-investment activities. Not surprisingly, high involvement VCs viewed their activities as more important.Based upon the amount of capital they managed, firms were also split into three groups. Average fund size varied from 278 to 12 million dollars. The larger firms had more professionals and managed more money per professional. The large firms provided the least, and the medium-sized firms the most, assistance to portfolio companies. Large firms also made larger individual investments. Even though they invested over half their funds in late-stage investments whereas smaller firms focused on the earlier stages, the large firms were still a major source of early stage financing.There were no differences between geographic regions in the proportion of investments where the venture capital firm served as lead investor. There were, however, major regional differences in investment stages of interest. Also differences were observed between regions that were not a result of differing size and investment stage.     

Choosing an optimal investment strategy: The role of robust pair-copulas based portfolios

This paper is concerned with the efficient allocation of a set of financial assets and its successful management. Efficient diversification of investments is achieved by inputing robust pair-copulas based estimates of the expected return and covariances in the mean-variance analysis of Markowitz. Although the whole point of diversifying a portfolio is to avoid rebalancing, very often one needs to rebalance to restore the portfolio to its original balance or target. But when and why to rebalance is a critical issue, and this paper investigates several managers' strategies to keep the allocations optimal. Findings for an emerging market target return and minimum risk investments are highly significant and convincing. Although the best strategy depends on the investor risk profile, it is empirically shown that the proposed robust portfolios always outperform the classical versions based on the sample estimates, yielding higher gains in the long run and requiring a smaller number of updates. We found that the pair-copulas based robust minimum risk portfolio monitored by a manager which checks its composition twice a year provides the best long run investment.     

Step Options

Motivated by risk management problems with barrier options, we propose a flexible modification of the standard knock‐out and knock‐in provisions and introduce a family of path‐dependent options: step options . They are parametrized by a finite knock‐out (knock‐in) rate , ρ. For a down‐and‐out step option, its payoff at expiration is defined as the payoff of an otherwise identical vanilla option discounted by the knock‐out factor exp(-ρτ_B^‐) or max(1‐ρτ^-B,0), where &\tau;_B^‐ is the total time during the contract life that the underlying price was lower than a prespecified barrier level ( occupation time ). We derive closed‐form pricing formulas for step options with any knock‐out rate in the range $[0,∞). For any finite knock‐out rate both the step option's value and delta are continuous functions of the underlying price at the barrier. As a result, they can be continuously hedged by trading the underlying asset and borrowing. Their risk management properties make step options attractive "no‐regrets" alternatives to standard barrier options. As a by‐product, we derive a dynamic almost‐replicating trading strategy for standard barrier options by considering a replicating strategy for a step option with high but finite knock‐out rate. Finally, a general class of derivatives contingent on occupation times is considered and closed‐form pricing formulas are derived.     

Climate change shocks and socially responsible investments

Climate change's impact on investor behavior is a scantly investigated area in finance. This paper examines the performance of socially responsible exchange trade funds (ETFs) concerning conventional ETFs, in response to climate change events. We proxy climate change signals with a list of natural disaster events that NASA scientists relate to climate change. We contribute to existing literature, by using a very extensive information set of ETF strategies, not influenced by rating agencies' subjective evaluation policies, and covering almost 90% of the universe of worldwide sustainability thematic-oriented ETFs. This sample allows us to identify the socially responsible investment behavior in response to unpredictable climate change shocks. Our identification strategy accounts for endogeneity concerns and relies on two-stage least square (2SLS) approach finding that responsible investors react to climate change events by purchasing socially responsible investments. The relationship between climate change signals and return of investment in themes linked to the development of sustainability is positive. Interestingly enough, the sign of this relationship is different, when we disentangle the empirical results according to the asset type, confirming that investors shift their investments from equity funds to bond funds when market sentiment worsens. Our results indicate that policymakers should increase the support of firms adopting environmentally conscious business practices, while managers should boost a sustainable business strategy.     

绿色指数发布的股价效应研究——基于投资者情绪的视角

近年来，承载着引导资金投向等多项使命，各类绿色指数相继发布，然而绿色指数是否真的对市场产生了影响有待验证。文章以2017-2019年绿色领先类公司股票数据为样本，采用事件研究法分析绿色指数发布后样本公司收益率的变化,借以探究绿色指数发布的股价效应。实证结果表明：在短期内，绿色指数发布对样本公司股价影响显著，指数发布后，公司的异常收益率在整体上显著为正。而长期来看，该股价效应不具备持续性，平均异常收益率会在长期回落。进一步，文章基于投资者情绪的视角，对该股价效应背后的影响机制做出了梳理。研究结果表明，绿色指数发布后，投资者情绪明显高涨，并且这种情绪对事件日后的异常收益有显著的正向影响。文章的研究为评价绿色指数发布的影响提供了良好的参考，同时对于内在机制的挖掘在一定程度上弥补了既有研究的不足。     

OPTIMAL CONSUMPTION AND PORTFOLIO SELECTION WITH INCOMPLETE MARKETS AND UPPER AND LOWER BOUND CONSTRAINTS

We study an optimal consumption and portfolio selection problem for an investor by a martingale approach. We assume that time is a discrete and finite horizon, the sample space is finite and the number of securities is smaller than that of the possible securities price vector transitions. the investor is prohibited from investing stocks more (less, respectively) than given upper (lower) bounds at any time, and he maximizes an expected time additive utility function for the consumption process. First we give a set of budget feasibility conditions so that a consumption process is attainable by an admissible portfolio process. Also we state the existence of the unique primal optimal solutions. Next we formulate a dual control problem and establish the duality between primal and dual control problems. Also we show the existence of dual optimal solutions. Finally we consider the computational aspect of dual approach through a simple numerical example.     

Retail investors and financial advisors: New evidence on trust and advice taking heuristics

This paper investigates factors that influence trust and advice taking among retail investors when consulting with financial advisors and making real-world portfolio decisions. The data reveal that non-expert retail investors trust their advisors a lot. Trust formation appears to be well described by a simple heuristic that relies substantially on the advisor's communication style when deciding how much to trust and delegate investment decisions. Portfolio decisions appear to depend more on investors' perceptions about the investor–advisor relationship than on the risk and return characteristics of investments comprising the portfolio choice set. This evidence supports Pentland's (2008) “honest signals” as a more powerful mechanism underlying investor trust than standard metrics based on past performance. Trust and advice-taking heuristics can be interpreted as well adapted to the environment of the non-profit bank cooperatives in which they are observed, implying that trusting based on simple honest signals, although vulnerable to exploitation, can be interpreted as ecologically rational. Features of the investor's environment typical of non-profit cooperative banks imply that the heuristics investors use can perform rather well without requiring investment experience or financial sophistication, which most investors in our sample are well aware they lack.     

Dispersion in Analysts’ Earnings Forecasts and Market Efficiency

Recent studies show that firms with higher analysts’ earnings forecasts dispersion subsequently have lower returns than firms with lower forecasts dispersion. This paper evaluates alternative explanations for the dispersion–return relation using a stochastic dominance approach. We aim to discriminate between the hypothesis that some asset pricing models can explain the puzzling negative relation between dispersion and stock returns, and the alternative hypothesis that the dispersion effect is mainly driven by investor irrationality and thus is an evidence of a failure of efficient markets. We find that low dispersion stocks dominate high dispersion stocks by second‐ and third‐order stochastic dominance over the period from 1976 to 2012. Our results imply that any investor who is risk‐averse and prefers positive skewness would unambiguously prefer low dispersion stocks to high dispersion stocks. We conclude that the dispersion effect is more likely evidence of market inefficiency, rather than a result of omitted risk factors.