TY - JOUR
T1 - Currency derivatives under a minimal market model with random scaling
AU - Heath, David
AU - Platen, Eckhard
PY - 2005/12
Y1 - 2005/12
N2 - This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is characterized by a random scaling, which provides for realistic exchange rate dynamics. The pricing of standard European options is studied. In particular, it is shown that the model produces implied volatility surfaces that are typically observed in real markets.
AB - This paper uses an alternative, parsimonious stochastic volatility model to describe the dynamics of a currency market for the pricing and hedging of derivatives. Time transformed squared Bessel processes are the basic driving factors of the minimal market model. The time transformation is characterized by a random scaling, which provides for realistic exchange rate dynamics. The pricing of standard European options is studied. In particular, it is shown that the model produces implied volatility surfaces that are typically observed in real markets.
KW - Currency derivatives
KW - Minimal market model
KW - Random scaling
KW - Stochastic volatility
UR - http://www.scopus.com/inward/record.url?scp=28844451087&partnerID=8YFLogxK
U2 - 10.1142/S0219024905003360
DO - 10.1142/S0219024905003360
M3 - Review article
SN - 0219-0249
VL - 8
SP - 1157
EP - 1177
JO - International Journal of Theoretical and Applied Finance
JF - International Journal of Theoretical and Applied Finance
IS - 8
ER -