𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Currency option pricing: Mean reversion and multi-scale stochastic volatility

✍ Scribed by Hoi Ying Wong; Jing Zhao

Publisher
John Wiley and Sons
Year
2010
Tongue
English
Weight
175 KB
Volume
30
Category
Article
ISSN
0270-7314

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

This paper investigates the valuation of currency options when the underlying currency follows a mean‐reverting lognormal process with multi‐scale stochastic volatility. A closed‐form solution is derived for the characteristic function of the log‐asset price. European options are then valued by means of the Fourier inversion formula. The proposed model enables us to calibrate simultaneously to the observed currency futures and the implied volatility surface of the currency options within a unified framework. The fractional fast Fourier transform (FFT) is adopted to implement the Fourier inversion, thus ensuring that the grid spacing restriction of the standard FFT can be relaxed, which results in a more efficient computation. Using Monte Carlo simulation as a benchmark, our numerical examples show that the derived option pricing formula is accurate and efficient for practical use. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark 30:938–956, 2010

📜 SIMILAR VOLUMES

Currency barrier option pricing with mea
Currency barrier option pricing with mean reversion
✍ C. H. Hui; C. F. Lo 📂 Article 📅 2006 🏛 John Wiley and Sons 🌐 English ⚖ 217 KB

## Abstract This article develops a barrier option pricing model in which the exchange rate follows a mean‐reverting lognormal process. The corresponding closed‐form solutions for the barrier options with time‐dependent barriers are derived. The numerical results show that barrier option values and

An explicitly solvable multi-scale stoch
An explicitly solvable multi-scale stochastic volatility model: Option pricing and calibration problems
✍ Lorella Fatone; Francesca Mariani; Maria Cristina Recchioni; Francesco Zirilli 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 457 KB

## Abstract We introduce an explicitly solvable multiscale stochastic volatility model that generalizes the Heston model. The model describes the dynamics of an asset price and of its two stochastic variances using a system of three Ito stochastic differential equations. The two stochastic variance

FFT based option pricing under a mean re
FFT based option pricing under a mean reverting process with stochastic volatility and jumps
✍ E. Pillay; J.G. O’Hara 📂 Article 📅 2011 🏛 Elsevier Science 🌐 English ⚖ 228 KB

Numerous studies present strong empirical evidence that certain financial assets may exhibit mean reversion, stochastic volatility or jumps. This paper explores the valuation of European options when the underlying asset follows a mean reverting log-normal process with stochastic volatility and jump

Pricing American options on foreign curr
Pricing American options on foreign currency with stochastic volatility, jumps, and stochastic interest rates
✍ Jia-Hau Guo; Mao-Wei Hung 📂 Article 📅 2007 🏛 John Wiley and Sons 🌐 English ⚖ 294 KB 👁 1 views

## Abstract 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 e