Binomial Option Pricing with Skewed Asset Returns

This research presents a method for estimating the parameters of the binomial option pricing model necessary to appropriately price calls on assets with asymmetric end-of-period return distributions. Parameters of the binomial model are shown to be a function of the mean, variance, and skewness of the underlying return distribution. It is also shown that failure to incorporate skewness results in the mispricing of the call.     

Option Pricing with Heterogeneous Expectations

This paper re-derives the finite mixture option pricing model of Ritchey (1990), based on the assumption that the option investors hold heterogeneous expectations about the parameters of the lognormal process of the underlying asset price. By proving that the model admits no riskless arbitrage, this paper justifies that the entire family of finite mixture of lognormal distributions is a desirable candidate set for recovering the risk-neutral probability distributions from contemporaneous options quotes. The parametric method derived from the model is significantly simpler than the nonparametric method of Rubinstein (1994) for recovering the risk-neutral probability distributions from contemporaneous option prices.     

A Non-Parametric Option Pricing Model: Theory and Empirical Evidence

In this paper, we propose an empirically-based, non-parametric option pricing model to evaluate S&P 500 index options. Given the fact that the model is derived under the real measure, an equilibrium asset pricing model, instead of no-arbitrage, must be assumed. Using the histogram of past S&P 500 index returns, we find that most of the volatility smile documented in the literature disappears.     

VIX期权定价与校正

VIX期权作为波动率衍生品能为金融机构提供有效的市场风险对冲工具。文献中对VIX期权定价的实证分析误差都很大,原因在于模型的选取误差以及校正方法和样本选取不妥。通过在VIX模型中加入均值回复因素和跳因素,可以使VIX过程更加合理,也可以使VIX期权定价精度更高。通过对VIX期权市场中间报价进行校正,得到了4个文献模型的参数估计,并比较4个模型的定价精度和正向隐含波动率偏斜拟合效果。     

The GARCH Option Pricing Model: A Modification of Lattice Approach

Ritchken and Trevor (1999) proposed a lattice approach for pricing American options under discrete time-varying volatility GARCH frameworks. Even though the lattice approach worked well for the pricing of the GARCH options, it was inappropriate when the option price was computed on the lattice using standard backward recursive procedures, even if the concepts of Cakici and Topyan (2000) were incorporated. This paper shows how to correct the deficiency and that with our adjustment, the lattice method performs properly for option pricing under the GARCH process. JEL Classification: C10, C32, C51, F37, G12     

Announcement Effects and Asymmetric Volatility in Industry Stock Returns: Evidence from Taiwan

This study employs financial econometric models to examine the asymmetric volatility of equity returns in response to monetary policy announcements in the Taiwanese stock market. The meetings of the board of directors at the Central Bank of the Republic of China (Taiwan) are considered for testing the announcement effects. The asymmetric generalized autoregressive conditional heteroskedasticity (GARCH) model and the smooth transition autoregression with GARCH model are used to measure equity returns' asymmetric volatility. We conclude that the asymmetric volatility of countercyclical equity returns can be identified. Our findings support the leverage effect of stock price changes for most industry equity returns in Taiwan.     

Interest Rate Derivatives in a Duffie and Kan Model with Stochastic Volatility: An Arrow-Debreu Pricing Approach

Simple analytical pricing formulae have been derived, by different authors and for several derivatives, under the Gaussian Langetieg (1980) model. The purpose of this paper is to use such exact Gaussian solutions in order to obtain approximate analytical pricing formulas under the most general stochastic volatility specification of the Duffie and Kan (1996) model. Using Gaussian Arrow-Debreu state prices, first order stochastic volatility approximate pricing solutions will be derived only involving one integral with respect to the time-to-maturity of the contingent claim under valuation. Such approximations will be shown to be much faster than the existing exact numerical solutions, as well as accurate.     

Option Pricing for Pure Jump Processes with Markov Switching Compensators

This paper proposes a model for asset prices which is the exponential of a pure jump process with an N-state Markov switching compensator. We argue that such a process has a good chance of capturing all the empirical stylized regularities of stock price dynamics and we provide a closed form representation of its characteristic function. We also provide a parsimonious representation of the (not necessarily unique) risk neutral density and show how to price and hedge a large class of options on assets whose prices follow this process.     

Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing

This paper discusses extensions of the implied diffusion approach of Dupire (1994) to asset processes with Poisson jumps. We show that this extension yields important model improvements, particularly in the dynamics of the implied volatility surface. The paper derives a forward PIDE (PartialIntegro-Differential Equation) and demonstrates how this equationcan be used to fit the model to European option prices. For numerical pricing of general contingent claims, we develop an ADI finite difference method that is shown to be unconditionally stable and, if combined with Fast Fourier Transform methods, computationally efficient. The paper contains several detailed examples fromthe S&P500 market. This revised version was published online in November 2006 with corrections to the Cover Date.     

Pricing dynamic binary variables and their derivatives

Many important assets or business ventures have cash flows that are not derivatives of a market security but are nevertheless dependent on some variable that is correlated with market prices. This includes many real option projects. This paper presents a methodology using a binary framework for pricing such assets by projection onto the market space. Under certain conditions, the result has the property that, given this price process, no risk-averse investor would choose to invest in this asset either long or short.     

Pricing credit-risky bonds and spread options modelling credit-spread term structures with two-dimensional Markov-modulated jump-diffusion

The relationship between company hazard rates and the business cycle becomes more apparent after a financial crisis. To address this relationship, a regime-switching process with an intensity function is adopted in this paper. In addition, the dynamics of both interest rates and asset values are modelled with a Markov-modulated jump-diffusion model, and a 2-factor hazard rate model is also considered. Based on this more suitable model setting, a closed-form model of pricing risky bonds is derived. The difference in yield between a risky bond and risk-free zero coupon bond is used to model a term structure of credit spreads (CSs) from which a closed-form pricing model of a call option on CSs is obtained. In addition, the degree to which the explicit regime shift affects CSs and credit-risky bond prices is numerically examined using three forward-rate functions under various business-cycle patterns.     

Real options under a double exponential jump-diffusion model with regime switching and partial information

We consider the irreversible investment in a project which generates a cash flow following a double exponential jump-diffusion process and its expected return is governed by a continuous-time two-state Markov chain. If the expected return is observable, we present explicit expressions for the pricing and timing of the option to invest. With partial information, i.e. if the expected return is unobservable, we provide an explicit project value and an integral-differential equation for the pricing and timing of the option. We provide a method to measure the information value, i.e. the difference between the option values under the two different cases. We present numerical solutions by finite difference methods. By numerical analysis, we find that: (i) the higher the jump intensity, the later the option to invest is exercised, but its effect on the option value is ambiguous; (ii) the option value increases with the belief in a boom economy; (iii) if investors are more uncertain about the economic environment, information is more valuable; (iv) the more likely the transition from boom to recession, the lower the value of the option; (v) the bigger the dispersion of the expected return, the higher the information value; (vi) a higher cash flow volatility induces a lower information value.     

The Effects of Transaction Costs and Different Borrowing and Lending Rates on the Option Pricing Model: A Note

This paper modifies the Black-Scholes option pricing model to include the effects of transaction costs and different borrowing and lending rates. The paper demonstrates that these market imperfections tend to offset each other yielding a bounded range of prices for each option. The paper also shows that under some conditions the option pricing hedge may be society's lowest cost financial intermediary.     

An International Asset Pricing Model with Time-Varying Hedging Risk

This paper employs a two-factor international equilibrium asset pricing model to examine the pricing relationships among the world's five largest equity markets. In addition to the traditional market factor premium, a hedging factor premium is included as the second factor to explain the relationship between risks and returns in the international stock markets. Moreover, a GARCH parameterization is adopted to characterize the general dynamics of the conditional second moments. The results suggest that the additional hedging risk premium is needed to explain rates of return on international equities. Furthermore, the restriction that the coefficient on the hedge-portfolio covariance is one smaller than the coefficient on the market-portfolio covariance can not be rejected. This suggests that the intertemporal asset pricing model proposed by Campbell (1993) can be used to explain the returns on the five largest stock market indices.     

Pricing of foreign exchange options under the MPT stochastic volatility model and the CIR interest rates

We consider an extension of the model proposed by Moretto, Pasquali, and Trivellato [2010. “Derivative Evaluation Using Recombining Trees under Stochastic Volatility.” Advances and Applications in Statistical Sciences 1 (2): 453–480] (referred to as the MPT model) for pricing foreign exchange (FX) options to the case of stochastic domestic and foreign interest rates driven by the Cox, Ingersoll, and Ross dynamics introduced in Cox, Ingersoll, and Ross [1985. “A Theory of Term Structure of Interest Rates.” Econometrica 53(2): 385–408]. The advantage of the MPT model is that it retains some crucial features of Heston's stochastic volatility model but, as demonstrated in Moretto, Pasquali, and Trivellato [2010. “Derivative Evaluation Using Recombining Trees under Stochastic Volatility.” Advances and Applications in Statistical Sciences 1 (2): 453–480], it is better suited for discretization through recombining lattices, and thus it can also be used to value and hedge exotic FX products. In the model examined in this paper, the instantaneous volatility is correlated with the exchange rate dynamics, but the domestic and foreign short-term rates are assumed to be mutually independent and independent of the dynamics of the exchange rate. The main result furnishes a semi-analytical formula for the price of the FX European call option, which hinges on explicit expressions for conditional characteristic functions.     

A Comparison of Option Prices Under Different Pricing Measures in a Stochastic Volatility Model with Correlation

This paper investigates option prices in an incomplete stochastic volatility model with correlation. In a general setting, we prove an ordering result which says that prices for European options with convex payoffs are decreasing in the market price of volatility risk.As an example, and as our main motivation, we investigate option pricing under the class of q-optimal pricing measures. The q-optimal pricing measure is related to the marginal utility indifference price of an agent with constant relative risk aversion. Using the ordering result, we prove comparison theorems between option prices under the minimal martingale, minimal entropy and variance-optimal pricing measures. If the Sharpe ratio is deterministic, the comparison collapses to the well known result that option prices computed under these three pricing measures are the same.As a concrete example, we specialize to a variant of the Hull-White or Heston model for which the Sharpe ratio is increasing in volatility. For this example we are able to deduce option prices are decreasing in the parameter q. Numerical solution of the pricing pde corroborates the theory and shows the magnitude of the differences in option price due to varying q.JEL Classification: D52, G13     

Pricing Bonds and Bond Options with Default Risk

The pricing of bonds and bond options with default risk is analysed in the general equilibrium model of Cox, Ingersoll, and Ross (1985). This model is extended by means of an additional parameter in order to deal with financial and credit risk simultaneously. The estimation of such a parameter, which can be considered as the market equivalent of an agencies' bond rating, allows to extract from current quotes the market perceptions of firm's credit risk. The general pricing model for defaultable zero-coupon bond is first derived in a simple discrete-time setting and then in continuous-time. The availability of an integrated model allows for the pricing of default-free options written on defaultable bonds and of vulnerable options written either on default-free bonds or defaultable bonds. A comparison between our results and those given by Jarrow and Turnbull (1995) is also presented.