Drift Estimation of Generalized Security Price Processes from High Frequency Derivative Prices

This paper presents a framework for using high frequency derivative prices to estimate the drift of generalized security price processes. This work may be seen more generally as a quasi-likelihood approach to estimating continuous-time parameters of derivative pricing models using discrete option data. We develop a generalized derivative-based estimator for the drift where the underlying security price process follows any arbitrary state-time separable diffusion process (including arithmetic and geometric Brownian motion as special cases). The framework provides a method to measure premia in derivative prices, test for risk-neutral pricing and leads to a new empirical approach to pricing derivative contingent claims. A sufficient condition for the asymptotic consistency of the generalized estimator is also obtained. A study based on generating the S&P500 index and calls shows that the estimator can correctly estimate the drift parameter. This revised version was published online in November 2006 with corrections to the Cover Date.     

The refinancing threshold pricing model: An economic approach to valuing MBS

Investigation of MBS prepayment data indicates that mortgagors have different interest rate levels, or thresholds, at which they exercise their option to prepay their mortgage. In order to properly value an MBS with heterogeneous mortgagors, Merrill Lynch has developed the Refinancing Threshold Pricing Model (RTP). The RTP model focuses on the refinancing decision of the mortgagor when pricing the mortgage pool. The model divides each pool into groups of mortgagors who share similar refinancing costs. Using market data, the RTP model endogenously determines both the implied costs that mortgagors face, as well as the proportion of the MBS pool in each refinancing cost group. In addition to determining pool value, the RTP model also calculates MBS duration, dP/dY and convexity. Comparison between RTP model values and actual market data reveals a strong correlation. The RTP has a wide range of applications, including valuing 15-year and 30-year conventional MBS; pricing interest-only (IO)/principal-only (PO) derivative MBS; determining new versus seasoned MBS price spreads; and valuing specific MBS pools.The information set forth was obtained from sources we believe reliable, but we do not guarantee its accuracy. Neither the information, nor any opinion expressed constitutes a solicitation by us for the purchase or sale of any securities or commodities. Merrill Lynch, Pierce, Fenner & Smith, Inc. or its affiliates may have either a long or short position in, and may buy and sell for its own account or the accounts of others, these securities.     

Unbiased and efficient Greeks of financial options

The price of a derivative security equals the discounted expected payoff of the security under a suitable measure, and Greeks are price sensitivities with respect to parameters of interest. When closed-form formulas do not exist, Monte Carlo simulation has proved very useful for computing the prices and Greeks of derivative securities. Although finite difference with resimulation is the standard method for estimating Greeks, it is in general biased and suffers from erratic behavior when the payoff function is discontinuous. Direct methods, such as the pathwise method and the likelihood ratio method, are proposed to differentiate the price formulas directly and hence produce unbiased Greeks (Broadie and Glasserman, Manag. Sci. 42:269–285, 1996). The pathwise method differentiates the payoff function, whereas the likelihood ratio method differentiates the densities. When both methods apply, the pathwise method generally enjoys lower variances, but it requires the payoff function to be Lipschitz-continuous. Similarly to the pathwise method, our method differentiates the payoff function but lifts the Lipschitz-continuity requirements on the payoff function. We build a new but simple mathematical formulation so that formulas of Greeks for a broad class of derivative securities can be derived systematically. We then present an importance sampling method to estimate the Greeks. These formulas are the first in the literature. Numerical experiments show that our method gives unbiased Greeks for several popular multi-asset options (also called rainbow options) and a path-dependent option.     

Are All Security Analysts Equal?

We examine the extent to which security analysts are homogeneous in their effect on firm valuation as measured by Tobin's Q. Earlier research documents a significant and positive relation between analyst coverage and firm valuation. We identify three classes of equity analysts and examine their differential effect on firm valuation associated with their coverage and their information production. We find that equity analysts are not homogeneous in their effect on firm valuation. The presence of analysts at national securities firms have the strongest effect on firm valuation followed by analysts at regional securities firms and finally analysts at nonbrokerage, or research, firms. We attribute this result to the differential monitoring and information dissemination function rendered by the analysts. Information produced by analysts, however, does not share the same credibility. Specifically, we find brokerage firms' buy recommendations are discounted by the market and have a weak effect on firm valuation. The results can be supported by arguments that brokerage firm analysts' recommendations are contaminated by their firms' investment banking relations with corporations.     

Potential measures and expected present value of operating costs until ruin in renewal risk models with general interclaim times

In this paper, a Sparre Andersen risk process with arbitrary interclaim time distribution is considered. We analyze various ruin-related quantities in relation to the expected present value of total operating costs until ruin, which was first proposed by Cai et al. [(2009a). On the expectation of total discounted operating costs up to default and its applications. Advances in Applied Probability 41(2), 495–522] in the piecewise-deterministic compound Poisson risk model. The analysis in this paper is applicable to a wide range of quantities including (i) the insurer's expected total discounted utility until ruin; and (ii) the expected discounted aggregate claim amounts until ruin. On one hand, when claims belong to the class of combinations of exponentials, explicit results are obtained using the ruin theoretic approach of conditioning on the first drop via discounted densities (e.g. Willmot [(2007). On the discounted penalty function in the renewal risk model with general interclaim times. Insurance: Mathematics and Economics 41(1), 17–31]). On the other hand, without any distributional assumption on the claims, we also show that the expected present value of total operating costs until ruin can be expressed in terms of some potential measures, which are common tools in the literature of Lévy processes (e.g. Kyprianou [(2014). Fluctuations of L'evy processes with applications: introductory lectures, 2nd ed. Berlin Heidelberg: Springer-Verlag]). These potential measures are identified in terms of the discounted distributions of ascending and descending ladder heights. We shall demonstrate how the formulas resulting from the two seemingly different methods can be reconciled. The cases of (i) stationary renewal risk model and (ii) surplus-dependent premium are briefly discussed as well. Some interesting invariance properties in the former model are shown to hold true, extending a well-known ruin probability result in the literature. Numerical illustrations concerning the expected total discounted utility until ruin are also provided.     

A risk-neutral equilibrium leading to uncertain volatility pricing

We study the formation of derivative prices in an equilibrium between risk-neutral agents with heterogeneous beliefs about the dynamics of the underlying. Under the condition that short-selling is limited, we prove the existence of a unique equilibrium price and show that it incorporates the speculative value of possibly reselling the derivative. This value typically leads to a bubble; that is, the price exceeds the autonomous valuation of any given agent. Mathematically, the equilibrium price operator is of the same nonlinear form that is obtained in single-agent settings with worst-case aversion against model uncertainty. Thus, our equilibrium leads to a novel interpretation of this price.     

Investment barriers and international asset pricing

In this article a multicountry model of international asset pricing is developed. This model incorporates a more general representation of the degree of segmentation in the international capital market. Specifically,N types of investors andN classes of securities are postulated. In general, thenth (n=1, 2, 3, ...N) type of investor has access to all security markets up to and including thenth class. Using the standard mean-variance framework, closed form equilibrium risk return relationships are obtained for all classes of securities. It is also shown that class 1 securities are priced as if markets are integrated, classn (n=2, 3 ...N) securities commandn different risk premia. Finally, the nature of the model specification allows us to investigate the effects of partial integration on investor welfare. It is shown that, in general, all investors prefer full integration to any form of partial integration.     

Derivatives securities: what they tell us

Jing Chen discusses how the study of derivatives securities provides a simple way of understanding financial markets and how derivative deals offer some early warning signals.     

Tainted portfolios: How impairment accounting rules restrict security sales

Contrary to claims that fair value accounting exacerbated banks’ securities sales during the recent financial crisis, we present evidence that suggests – if anything – that the current impairment accounting rules served as a deterrent to selling. Specifically, because banks must provide evidence of their ‘intent and ability’ to hold securities with unrealized losses, there are strong incentives to reduce, rather than increase, security sales when market values decline to avoid ‘tainting’ their remaining securities portfolio. Validating this concern, we find that banks incur greater other‐than‐temporary impairment (OTTI) charges when they sell more securities. We then find that banks sell fewer securities when their security portfolios have larger unrealized losses (and thus larger potential impairment charges), and these results are concentrated in banks with homogenous securities portfolios, expert auditors, more experienced managers, and greater regulatory capital slack. Overall, our results suggest that – contrary to critics’ claims – the accounting rules appear to have reduced banks’ propensity to sell their securities during the financial crisis.     

On the analysis of a multi-threshold Markovian risk model

We consider a class of Markovian risk models perturbed by a multiple threshold dividend strategy in which the insurer collects premiums at rate c _i whenever the surplus level resides in the i-th surplus layer, i=1, 2, …,n+1 where n<∞. We derive the Laplace-Stieltjes transform (LST) of the distribution of the time to ruin as well as the discounted joint density of the surplus prior to ruin and the deficit at ruin. By interpreting that the insurer, whose gross premium rate is c, pays dividends continuously at rate d _i =c?c _i whenever the surplus level resides in the i-th surplus layer, we also derive the expected discounted value of total dividend payments made prior to ruin. Our results are obtained via a recursive approach which makes use of an existing connection, linking an insurer's surplus process to an embedded fluid flow process.     

Shorting in Speculative Markets

In models of trading with heterogeneous beliefs following Harrison-Kreps, short selling is prohibited and agents face constant marginal costs-of-carry. The resale option guarantees that prices exceed buy-and-hold prices and the difference is identified as a bubble. We propose a model where risk-neutral agents face asymmetric increasing marginal costs on long and short positions. Here, agents also value an option to delay, and a Hamilton-Jacobi-Bellman equation quantifies the influence of costs on prices. An unexpected decrease in shorting costs may deflate a bubble, linking financial innovations that facilitated shorting of mortgage-backed securities to the collapse of prices.     

Maximal submarkets that replicate any option

In this article we study the replication of options in security markets X with a finite number of states. Specifically, we study the existence of maximal submarkets (subspaces) Y of X so that any option written on the elements of Y is replicated by a marketed asset x of X. So inside these subspaces the pricing problem is simple because any option is priced by the replicating portfolio. Using the theory of lattice-subspaces and positive bases developed by Polyrakis (Trans Am Math Soc 348:2793–2810, 1996; 351:4183–4203, 1999), we identify the set of all maximal replicated subspaces. In particular, for any maximal replicated subspace we determine a positive basis of the subspace. Moreover we show that the union of all maximal replicated subspaces is the set of all marketed securities x ? X{x\in X} so that any option written on x is replicated. So we determine also the set of securities with replicated options.     

Semi-analytical MBS Pricing

This paper presents a multi-factor valuation model for fixed-rate callable mortgage backed securities (MBS). The model yields semi-analytic solutions for the value of MBS in the sense that the MBS value is found by solving a system of ordinary differential equations. Instead of modelling the conditional prepayment rate (CPR), as is customary, the pool size is the primary modelling object. It is shown that the value of a single MBS payment due at time t _n can be found by computing two expectations of the pool size at time t _n–1 and t _n respectively. This is a general result independent of any interest rate model. However, if the pool size is specified in a way that makes the expectations solvable using transform methods, semi-analytic pricing formulas are achieved. The affine and quadratic pricing frameworks are combined to get flexible and sophisticated prepayment functions. We show that the model has no problem of generating negative convexity as the spot rate falls, and still be close to a similar non-callable bond when the spot rate rises.     

Perquisites,Risk, and Capital Structure

In a corporate agency problem, perquisites and risk interact to produce novel, complex comparative statics. For example, even if additional debt induces risk-neutral insiders to increase risk, they never seek to increase the market value of their stock; instead, insiders decrease the present value of their subsequent, conditionally optimal perquisites. Also, the firm's optimal capital structure includes a risky bond with an agreement to remove insiders whenever the bond defaults. However, the optimal sharing rule between corporate claimants cannot be supported solely by standard securities such as bonds, stocks, options, and their hybrids.     

A note on the importance of overnight information in risk management models

This paper examines the economic value of overnight information to users of risk management models. In addition to the information revealed by overseas markets that trade during the (domestic) overnight period, this paper exploits information generated via recent innovations in the structure of financial markets. In particular, certain securities (and associated derivative products) can now be traded at any time over a 24-h period. As such, it is now possible to make use of information generated by trading, in (almost) identical securities, during the overnight period. Of the securities that are available over such time periods, S&P 500 related products are by far the most actively traded and are, therefore, the subject of this paper. Using a variety of conditional volatility models that allow time-dependent information flow within (and across) three different S&P 500 markets, the results show that overnight information flow has a significant impact on the conditional volatility of daytime traded S&P 500 securities. Moreover (time-consistent) forecasts from models that incorporate overnight information are shown to have economic value to risk managers. In particular, Value-at-Risk (VaR) models based on these conditional volatility models are shown to be more accurate than VaR models that ignore overnight information.     

Financial innovation, values and volatilities when markets are incomplete

The traditional pricing methodology in finance values derivative securities as redundant assets that have no impact on equilibrium prices and allocations. This paper considers a model with incomplete markets in which the valuation of derivative securities cannot be treated independently from the valuation of the primary securities. The model constitutes a framework for the analysis of the consequences of financial innovation (creation of new contracts or modification of existing contracts). We provide a numerical counterexample to the popular belief that financial innovations that increase the volatilities of traded securities are bad. In this example the introduction of an option increases the volatility of the rate of return on the underlying stock, yet the creation of this asset is unanimously supported by investors.I am grateful to H. Polemarchakis and to an anonymous referee for insightful suggestions.     

Derivatives and systemic risk: Netting, collateral, and closeout

In the U.S., as in most countries with well-developed securities markets, derivative securities enjoy special protections under insolvency resolution laws. Most creditors are “stayed” from enforcing their rights while a firm is in bankruptcy. However, many derivatives contracts are exempt from these stays. Furthermore, derivatives enjoy netting and closeout, or termination, privileges which are not always available to most other creditors. The primary argument used to motivate passage of legislation granting these extraordinary protections is that derivatives markets are a major source of systemic risk in financial markets and that netting and closeout reduce this risk. To date, these assertions have not been subjected to rigorous economic scrutiny. This paper critically re-examines this hypothesis. These relationships are more complex than often perceived. We conclude that it is not clear whether netting, collateral, and/or closeout lead to reduced systemic risk, once the impact of these protections on the size and structure of the derivatives market has been taken into account.     

Looking Beyond Credit Ratings: Factors Investors Consider In Pricing European Asset‐Backed Securities

In this paper, we empirically investigate what credit factors investors rely upon when pricing the spread at issue for European asset‐backed securities. More specifically, we investigate how credit factors affect new issuance spreads after taking into account credit rating. We do so by investigating primary market spreads for tranches of non‐mortgage‐related asset‐backed securities issued from 1999 to the year prior to the subprime mortgage crisis, 2007. We find that although credit ratings play a major role in determining spreads, investors appear to not rely exclusively on these ratings. Our findings strongly suggest that investors do not ignore other credit factors beyond the assigned credit rating.     

Financial Intermediaries and the Cross‐Section of Asset Returns

Financial intermediaries trade frequently in many markets using sophisticated models. Their marginal value of wealth should therefore provide a more informative stochastic discount factor (SDF) than that of a representative consumer. Guided by theory, we use shocks to the leverage of securities broker‐dealers to construct an intermediary SDF. Intuitively, deteriorating funding conditions are associated with deleveraging and high marginal value of wealth. Our single‐factor model prices size, book‐to‐market, momentum, and bond portfolios with an R² of 77% and an average annual pricing error of 1%—performing as well as standard multifactor benchmarks designed to price these assets.     

Analysis of a threshold dividend strategy for a MAP risk model

We consider a class of Markovian risk models in which the insurer collects premiums at rate c₁(c₂) whenever the surplus level is below (above) a constant threshold level b. We derive the Laplace-Stieltjes transform (LST) of the distribution of the time to ruin as well as the LST (with respect to time) of the joint distribution of the time to ruin, the surplus prior to ruin, and the deficit at ruin. By interpreting that the insurer pays dividends continuously at rate c₁?c₂ whenever the surplus level is above b, we also derive the expected discounted value of total dividend payments made prior to ruin. Our results are obtained by making use of an existing connection which links an insurer's surplus process to an embedded fluid flow process.