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Stochastic Interest Rate (stochastic + interest_rate)
Selected AbstractsTesting Option Pricing Models with Stochastic Volatility, Random Jumps and Stochastic Interest RatesINTERNATIONAL REVIEW OF FINANCE, Issue 3-4 2002George J. Jiang In this paper, we propose a parsimonious GMM estimation and testing procedure for continuous-time option pricing models with stochastic volatility, random jump and stochastic interest rate. Statistical tests are performed on both the underlying asset return model and the risk-neutral option pricing model. Firstly, the underlying asset return models are estimated using GMM with valid statistical tests for model specification. Secondly, the preference related parameters in the risk-neutral distribution are estimated from observed option prices. Our findings confirm that the implied risk premiums for stochastic volatility, random jump and interest rate are overall positive and varying over time. However, the estimated risk-neutral processes are not unique, suggesting a segmented option market. In particular, the deep ITM call (or deep OTM put) options are clearly priced with higher risk premiums than the deep OTM call (or deep ITM put) options. Finally, while stochastic volatility tends to better price long-term options, random jump tends to price the short-term options better, and option pricing based on multiple risk-neutral distributions significantly outperforms that based on a single risk-neutral distribution. [source] Optimal investment problem with stochastic interest rate and stochastic volatility: Maximizing a power utilityAPPLIED STOCHASTIC MODELS IN BUSINESS AND INDUSTRY, Issue 3 2009Jinzhu Li Abstract In this paper, we assume that an investor can invest his/her wealth in a bond and a stock. In our wealth model, the stochastic interest rate is described by a Cox,Ingersoll,Ross (CIR) model, and the volatility of the stock is proportional to another CIR process. We obtain a closed-form expression of the optimal policy that maximizes a power utility. Moreover, a verification theorem without the usual Lipschitz assumptions is proved, and the relationships between the optimal policy and various parameters are given. Copyright © 2009 John Wiley & Sons, Ltd. [source] A generalization of Rubinstein's "Pay now, choose later"THE JOURNAL OF FUTURES MARKETS, Issue 5 2008Jia-Hau Guo This article provides quasi-analytic pricing formulae for forward-start options under stochastic volatility, double jumps, and stochastic interest rates. Our methodology is a generalization of the Rubinstein approach and can be applied to several existing option models. Properties of a forward-start option may be very different from those of a plain vanilla option because the entire uncertainty of evolution of its price is cut off by the strike price at the time of determination. For instance, in contrast to the plain vanilla option, the value of a forward-start option may not always increase as the maturity increases. It depends on the current term structure of interest rates. © 2008 Wiley Periodicals, Inc. Jrl Fut Mark 28:488,515, 2008 [source] Pricing American options on foreign currency with stochastic volatility, jumps, and stochastic interest ratesTHE JOURNAL OF FUTURES MARKETS, Issue 9 2007Jia-Hau Guo By applying the Heath,Jarrow,Morton (HJM) framework, an analytical approximation for pricing American options on foreign currency under stochastic volatility and double jump is derived. This approximation is also applied to other existing models for the purpose of comparison. There is evidence that such types of jumps can have a critical impact on earlyexercise premiums that will be significant for deep out-of-the-money options with short maturities. Moreover, the importance of the term structure of interest rates to early-exercise premiums is demonstrated as is the sensitivity of these premiums to correlation-related parameters. © 2007 Wiley Periodicals, Inc. Jrl Fut Mark 27:867,891, 2007 [source] | ||||||||||