Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models

This paper demonstrates how to value American interest rate options under the jump-extended constant-elasticity-of-variance (CEV) models. We consider both exponential jumps (see Duffie et al., 2000) and lognormal jumps (see Johannes, 2004) in the short rate process. We show how to superimpose recombining multinomial jump trees on the diffusion trees, creating mixed jump-diffusion trees for the CEV models of short rate extended with exponential and lognormal jumps. Our simulations for the special case of jump-extended Cox, Ingersoll, and Ross (CIR) square root model show a significant computational advantage over the Longstaff and Schwartz’s (2001) least-squares regression method (LSM) for pricing American options on zero-coupon bonds.     

Investor sentiment and interest rate volatility smile: evidence from Eurodollar options markets

This paper studies the extent to which investor sentiment affects the Eurodollar option smile and finds that there is the dynamic interplay between sentiment-driven investors and arbitrageurs. The results reveal a significant relation between investor sentiment and interest rate volatility smile. The significant relations are stronger for put options, for short-maturity options, and for periods with higher uncertainty. The results are robust when considering controlling variables, net buying pressure, different interest rate option models, model-free method, or excluding rational components from the sentiment measures. Our findings favor the limits to arbitrage hypothesis against the positive feedback hypothesis, suggesting that the sentiment effect is transitory. Change in investor sentiment explains the time-varying smile that can be explained neither by rational interest rate models nor by net buying pressure.     

Quadratic hedging in affine stochastic volatility models

We determine the variance-optimal hedge for a subset of affine processes including a number of popular stochastic volatility models. This framework does not require the asset to be a martingale. We obtain semiexplicit formulas for the optimal hedging strategy and the minimal hedging error by applying general structural results and Laplace transform techniques. The approach is illustrated numerically for a Lévy-driven stochastic volatility model with jumps as in Carr et al. (Math Finance 13:345–382, 2003).      

Autoregressive stochastic volatility models with heavy-tailed distributions: A comparison with multifactor volatility models

This paper examines two asymmetric stochastic volatility models used to describe the heavy tails and volatility dependencies found in most financial returns. The first is the autoregressive stochastic volatility model with Student's t-distribution (ARSV-t), and the second is the multifactor stochastic volatility (MFSV) model. In order to estimate these models, the analysis employs the Monte Carlo likelihood (MCL) method proposed by Sandmann and Koopman [Sandmann, G., Koopman, S.J., 1998. Estimation of stochastic volatility models via Monte Carlo maximum likelihood. Journal of Econometrics 87, 271–301.]. To guarantee the positive definiteness of the sampling distribution of the MCL, the nearest covariance matrix in the Frobenius norm is used. The empirical results using returns on the S&P 500 Composite and Tokyo stock price indexes and the Japan–US exchange rate indicate that the ARSV-t model provides a better fit than the MFSV model on the basis of Akaike information criterion (AIC) and the Bayes information criterion (BIC).     

Pricing mortgage-backed securities in a multifactor interest rate environment: a multivariate density estimation approach

Multivariate density estimation (MDE) suggests that mortgage-backedsecurity (MBS) prices can be well described as a function ofthe level and slope of the term structure. We analyze how thisfunction varies across MBSs with different coupons. An importantfinding is that the interest rate level proxies for the moneynessof the option, the expected level of prepayments, and the averagelife of the cash flows, while the term structure slope controlsfor the average rate at which these cash flows should be discounted.     

Regime shifts in interest rate volatility

I find evidence of regime shifts in interest rate volatility using short-rate data from the U.S., the U.K., Japan, and Canada. The regime shifts, if unaccounted for, could lead to spurious volatility persistence when the volatility processes are estimated with the stochastic volatility (SVOL) model. In contrast, the apparent persistence in volatility drops sharply in three out of the four countries when I estimate the volatility processes with the regime-switching stochastic volatility (RSSV) model. I also contribute to the literature by showing how to account for correlation in the regime-switching stochastic volatility model, which is important for modeling asymmetric volatility.     

Multi-stage real option evaluation with double barrier under stochastic volatility and interest rate

Annals of Finance - This paper focuses on valuing R&D projects using a twofold compound real option by including two knock-out barriers. However, the valuation of R&D projects is...     

Explaining the volatility smile: non-parametric versus parametric option models

We employ a “non-parametric” pricing approach of European options to explain the volatility smile. In contrast to “parametric” models that assume that the underlying state variable(s) follows a stochastic process that adheres to a strict functional form, “non-parametric” models directly fit the end distribution of the underlying state variable(s) with statistical distributions that are not represented by parametric functions. We derive an approximation formula which prices S&P 500 index options in closed form which corresponds to the lower bound recently proposed by Lin et al. (Rev Quant Financ Account 38(1):109–129, 2012). Our model yields option prices that are more consistent with the data than the option prices that are generated by several widely used models. Although a quantitative comparison with other non-parametric models is more difficult, there are indications that our model is also more consistent with the data than these models.     

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.     

Pricing via recursive quantization in stochastic volatility models

We provide the first recursive quantization-based approach for pricing options in the presence of stochastic volatility. This method can be applied to any model for which an Euler scheme is available for the underlying price process and it allows one to price vanillas, as well as exotics, thanks to the knowledge of the transition probabilities for the discretized stock process. We apply the methodology to some celebrated stochastic volatility models, including the Stein and Stein [Rev. Financ. Stud. 1991, (4), 727–752] model and the SABR model introduced in Hagan et al. [Wilmott Mag., 2002, 84–108]. A numerical exercise shows that the pricing of vanillas turns out to be accurate; in addition, when applied to some exotics like equity-volatility options, the quantization-based method overperforms by far the Monte Carlo simulation.     

Alternative asset-price dynamics and volatility smile

Abstract

We review the general class of analytically tractable asset-price models that was introduced by Brigo and Mercurio (2001a Mathematical Finance—Bachelier Congr. 2000 (Springer Finance) ed H Geman, D B Madan, S R Pliska and A C F Vorst (Berlin: Springer) pp 151–74), where the considered asset can be an exchange rate, a stock index or even a forward Libor rate. The class is based on an explicit SDE under a given forward measure and includes models featuring (i) explicit asset-price dynamics, (ii) a virtually unlimited number of parameters and (iii) analytical formulae for European options.

We also review the fundamental case where the asset-price density is given, at every time, by a mixture of log-normal densities with equal means. We then introduce two other cases: the first is still based on log-normal densities, but it allows for different means in the distributions; the second is based on processes of hyperbolic-sine type.

Finally, we test the goodness of calibration to real market data of the considered models, choosing a particularly asymmetric volatility surface. As expected, the model based on hyperbolic-sine density mixtures achieves the lowest calibration error.     

Regime switches in exchange rate volatility and uncovered interest parity

We use a regime-switching model to examine how exchange rate volatility is related to the failure of uncovered interest parity. Main findings are as follows. First, exchange rate returns are strongly influenced by regime switches in the relationship between the returns and interest rate differentials. Second, low-yielding currencies appreciate less frequently, but once it occurs, their movements are faster than when they depreciate. Third, depreciation of low-yielding currencies and low volatility are mutually dependent on each other. Finally, these three findings are more evident for shorter horizons. The second and third results are consistent with a market participants’ view: short-term carry trades in a low-volatility environment and their rapid unwinding substantially influence exchange rates. We consider the effects of funding liquidity to explain these results.     

Pricing and hedging power options

In this paper we study the pricing and hedging of options whose payoff is a polynomial function of the underlying price at expiration; so-called ‘power options’. Working in the well-known Black and Scholes (1973) framework we derive closed-form formulas for the prices of general power calls and puts. Parabola options are studied as a special case. Power options can be hedged by statically combining ordinary options in such a way that their payoffs form a piecewise linear function which approximates the power option's payoff. Traditional delta hedging may subsequently be used to reduce any residual risk.     

Modelling and forecasting short-term interest rate volatility: A semiparametric approach

This paper employs a semiparametric procedure to estimate the diffusion process of short-term interest rates. The Monte Carlo study shows that the semiparametric approach produces more accurate volatility estimates than models that accommodate asymmetry, level effect and serial dependence in the conditional variance. Moreover, the semiparametric approach yields robust volatility estimates even if the short rate drift function and the underlying innovation distribution are misspecified. Empirical investigation with the U.S. three-month Treasury bill rates suggests that the semiparametric procedure produces superior in-sample and out-of-sample forecast of short rate changes volatility compared with the widely used single-factor diffusion models. This forecast improvement has implications for pricing interest rate derivatives.     

Pricing participating policies under the Meixner process and stochastic volatility

We propose a model for the valuation of participating life insurance products under the Meixner process, which belongs to the family of semi-heavy tailed processes. This particular model assumption is extremely desirable as it captures the stylised features of the return distribution, with existing moment generating functions. The highlight of the paper is the analytical solution derived for minimising the relative entropy between the historical and risk-neutral measures, when driving a pricing kernel. Further, we capture the stochastic volatility effect using an accurate polynomial approximation technique. Finally, to highlight the practical applications, we conduct a simulation experiment.     

关于Shibor利率期权波动率定价机制的研究

Shibor自2007年发布以来,已成为人民币利率市场的一个重要定价基准,对金融衍生品、债券的定价起着十分重要的作用,由于人民币利率衍生品市场尚处于发展的初期,与美元Libor利率期权等较为成熟市场相比,目前Shibor利率期权缺少成熟的市场报价。本文通过风险中性的定价方程反解参数的方法,利用Shibor利率掉期曲线对Shibor利率上下限期权的隐含波动率进行计算,从而探讨对Shibor利率期权的定价。