A semi-analytic method for valuing high-dimensional options on the maximum and minimum of multiple assets

Valuing high-dimensional options has many important applications in finance but when the true distributions are unknown or complex, numerical approximations must be used. Approximation methods based on Monte-Carlo simulation show a steep trade-off between estimation accuracy and computational efficiency. This article presents an alternative semi-analytic approximation method for pricing options on the maximum or minimum of multiple assets with unknown distributions. Computational efficiency is shown to improve significantly without sacrificing estimation accuracy. The method is illustrated with applications to options on underlying assets with mean-reverting prices, time-dependent correlations, and stochastic volatility The authors would like to thank the two anonymous referees, the associate editor, and Dr. Jess H. Chua at the University of Calgary for valuable comments and insights on this research. This research was partly supported by NUS grant R-146-000-059-112     

Assessing the Least Squares Monte-Carlo Approach to American Option Valuation

A detailed analysis of the Least Squares Monte-Carlo (LSM) approach to American option valuation suggested in Longstaff and Schwartz (2001) is performed. We compare the specification of the cross-sectional regressions with Laguerre polynomials used in Longstaff and Schwartz (2001) with alternative specifications and show that some of these have numerically better properties. Furthermore, each of these specifications leads to a trade-off between the time used to calculate a price and the precision of that price. Comparing the method-specific trade-offs reveals that a modified specification using ordinary monomials is preferred over the specification based on Laguerre polynomials. Next, we generalize the pricing problem by considering options on multiple assets and we show that the LSM method can be implemented easily for dimensions as high as ten or more. Furthermore, we show that the LSM method is computationally more efficient than existing numerical methods. In particular, when the number of assets is high, say five, Finite Difference methods are infeasible, and we show that our modified LSM method is superior to the Binomial Model.     

发电企业上市公司引用股票期权激励机制探讨

分析了股票期权激励制度给上市公司带来的效益以及在中国的应用模式,并按九个方面阐述了股票期权激励制度设计。     

Timing of earnings restatements: CEO equity compensation and market reaction

This study investigates the impact of chief executive officers’ (CEO) compensation on their choices regarding the timing of earnings restatements. The results indicate a negative relationship between options exercised and lags in disclosing the restated earnings, suggesting that managers who exercise options in a given year tend to release information quickly. This effect is more pronounced if the options are exercised after the dark period. We also find that the market penalises longer lags in the restatement disclosure. It seems that the CEO would try to optimise the timing of information release so as to balance the costs and benefits.     

REAL OPTIONS AND THE CROSS‐SECTION OF EXPECTED STOCK RETURNS

This paper surveys the theoretical literature investigating the effect of firms’ investment flexibility on the cross‐section of expected stock returns. Real options analysis derives firms’ value‐maximizing investment policies as functions of exogenous fundamental drivers of profitability and calculates firms’ market values as functions of the same variables. These functions yield the relationship between expected stock returns and firm fundamentals. Several plausible explanations for the value premium – the high average stock returns earned by firms with high book‐to‐market ratios – emerge from this literature.     

Real options and contingent convertibles with regime switching

We consider a firm with no assets in place but an option to invest in a project. The investment is irreversible but delayable in a regime-switching economy. The firm issues equity, straight bonds (SBs) and contingent convertibles (CoCos). We provide the closed-form prices for the firm׳s securities and the pricing and timing of the option. Our numerical analyses discover that issuing CoCos instead of SBs induces much less agency cost of debt. The agency cost is higher in a boom economy than in recession but the difference is small. There is a unique CoCos׳ conversion ratio such that the agency cost arrives at the minimum value zero. The inefficiencies arising from asset substitution and debt overhang are much more significant in recession than in boom. Only if the conversion ratio is not too small, the two inefficiencies disappear during boom periods. While the effects of the conversion rate on optimal capital structure and firm value and those of supervision and jump intensity on optimal CoCos׳ coupon are ambiguous and weak, the stricter the supervision or the longer the economy remains in recession, the less the option value and the optimal SBs׳ coupon.     

How much is the gap?—Efficient jump risk-adjusted valuation of leveraged certificates

This paper develops a novel and highly efficient numerical algorithm for the gap risk-adjusted valuation of leveraged certificates. The existing literature relies on Monte Carlo simulations, which are not fast enough to be used in a market-making environment. This is because issuers need to compute thousands of price updates per second. By valuing leveraged certificates as multi-window barrier options, we explicitly model random jumps that occur at known times, such as between the exchange closing and re-opening. Our algorithm combines the one-day transition probability with Simpson’s numerical integration rule. This yields a backward induction scheme which requires a significantly coarser spatial and time grid than finite-difference methods. We confirm its robustness and accuracy through Monte Carlo simulations.     

Geometric Asian option pricing in general affine stochastic volatility models with jumps

In this paper, we present some results on Geometric Asian option valuation for affine stochastic volatility models with jumps. We shall provide a general framework into which several different valuation problems based on some average process can be cast, and we shall obtain closed form solutions for some relevant affine model classes.     

Stock markets’ bubbles burst and volatility spillovers in agricultural commodity markets

Our paper focuses on commodity financialization and the gradual integration between commodity and financial markets, investigating to what extent shocks in stock markets impact commodity price volatility, and the persistency of the phenomenon. To this end, we estimate Volatility Impulse Response Function from stock markets to agricultural commodity markets over a symmetric window before and after two of the most important bubble bursts since the new millennium, the 2000 dot.com bubble and the 2008 financial crises. Results highlight that volatility spillover increased significantly after the 2008 financial crises, signalling a rising interconnection between financial and agricultural commodity markets.     

Pricing executive stock options with averaging features under the Heston–Nandi GARCH model

In this paper, we focus on the pricing issue of four types of executive stock options (ESOs) in the Heston–Nandi generalized autoregressive conditional heteroskedasticity option pricing model. Based on the derived benchmark strike prices in the proposed framework, we obtain the closed-form pricing formulae for four types of ESOs. In the numerical part, we investigate the sensitivity and cost efficiency of ESOs and suggest that systematic risk (stock β) and the fraction of wealth invested in restricted stock could impede the cost efficiency of ESOs.