New approximations in local volatility models
نویسندگان
چکیده
For general time-dependent local volatility models, we propose new approximation formulas for the price of call options. This extends previous results of [BGM10b] where stochastic expansions combined with Malliavin calculus were performed to obtain approximation formulas based on the local volatility At The Money. Here, we derive alternative expansions involving the local volatility at strike. Averaging both expansions give even more accurate results. Approximations of the implied volatility are provided as well.
منابع مشابه
Modeling Stock Return Volatility Using Symmetric and Asymmetric Nonlinear State Space Models: Case of Tehran Stock Market
Volatility is a measure of uncertainty that plays a central role in financial theory, risk management, and pricing authority. Turbulence is the conditional variance of changes in asset prices that is not directly observable and is considered a hidden variable that is indirectly calculated using some approximations. To do this, two general approaches are presented in the literature of financial ...
متن کاملAnalytical formulas for local volatility model with stochastic rates
This paper presents new approximation formulae of European options in a local volatility model with stochastic interest rates. This is a companion paper to our work on perturbation methods for local volatility models in Benhamou et al. (2009c) for the case of stochastic interest rates. The originality of this approach is to model the local volatility of the discounted spot and to obtain accurat...
متن کاملA Taylor series approach to pricing and implied vol for LSV models
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no special functions, no infinite series and no numerical integration). As such, app...
متن کاملPortfolio Optimization under Local-Stochastic Volatility: Coefficient Taylor Series Approximations & Implied Sharpe Ratio
We study the finite horizonMerton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the ‘implied Sharpe ratio’ and derive a series approximation for this quantity. The zeroth-order approximation of the value fu...
متن کاملPortfolio Optimization under Local-Stochastic Volatility: Coefficient Taylor Series Approximations and Implied Sharpe Ratio
We study the finite horizonMerton portfolio optimization problem in a general local-stochastic volatility setting. Using model coefficient expansion techniques, we derive approximations for the both the value function and the optimal investment strategy. We also analyze the ‘implied Sharpe ratio’ and derive a series approximation for this quantity. The zeroth-order approximation of the value fu...
متن کامل