Q4. Swaptions

a) Use the Smith (1991) multiplier applied to the Black (1976) method to calculate the price of a Payer Swaption knowing the following information:

- A 2-year Payer Swaption written on a 4-year Swap

- Half-year composition

- Forward swap rate starting in 2 years and ending in 6 years: 8.9%

- Exercise rate: 7.5%

- Risk-free rate: 2.59%

- The volatility of the forward sawp per year: 24%

- Swap principal: $2,000,000

b) A similar method could be used to calculate a call on an electricity swap. Explain.