Pricing Hybrid Derivatives in the LIBOR Market Model

Hybrid Derivatives

PRDC (Power Reverse Dual Currency)

Nikkei 225 Linked Multi-Callable

　　　　　　 Maturity 20-30 years

Risks in Hybrid derivatives

• Volatility skew/smile of underlying

• Correlation between underlying and interest rates

Hybrid LIBOR Market Model

• Spot FX rate

• Domestic Forward LIBOR Rates

Hybrid LIBOR Market Model

• Foreign forward LIBOR rates

FX Option Price

• Forward FX Rate

• FX Call Option Price

Asymptotic Expansion Method

• Simple example

• Taylor’s series expansion

Asymptotic FX Option Formula

• Forward FX rate

• Domestic forward LIBOR rates

• Foreign forward LIBOR rates

• Third order asymptotic expansion of forward FX rate