Valuation and hedging strategy of currency options under regime-switching jump-diffusion model

The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modulated jump-diffusion model. The domestic and foreign money market interest rates, t...

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Bibliographic Details
Published in:Acta Mathematicae Applicatae Sinica 2017-10, Vol.33 (4), p.871-892
Main Authors: Chen, Shou-ting, Diao, Xun-di, Zhu, Ai-lin
Format: Article
Language:English
Subjects:
Applications of Mathematics
Computer simulation
Currency options
Differential equations
Diffusion rate
Economic models
Foreign exchange rates
Hedging
Integral equations
Interest rates
Markets
Markov chains
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Risk analysis
Securities prices
Switching
Theoretical
Volatility
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Summary:The main purpose of this thesis is in analyzing and empirically simulating risk minimizing European foreign exchange option pricing and hedging strategy when the spot foreign exchange rate is governed by a Markov-modulated jump-diffusion model. The domestic and foreign money market interest rates, the drift and the volatility of the exchange rate dynamics all depend on a continuous-time hidden Markov chain which can be interpreted as the states of a macro-economy. In this paper, we will provide a practical lognormal diffusion dynamic of the spot foreign exchange rate for market practitioners. We employing the minimal martingale measure to demonstrate a system of coupled partial-differential-integral equations satisfied by the currency option price and attain the corresponding hedging schemes and the residual risk. Numerical simulations of the double exponential jump diffusion regime-switching model are used to illustrate the different effects of the various parameters on currency option prices.
ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-017-0704-z