European Currency Option Analytics
The previous chapter developed the industry-standard Black-Scholes-Merton (BSM) model for European currency options. Attention now turns to using the model to understand the dynamics of option valuation and the analysis of option risk.
In the BSM model, five factors contribute to the valuation of a currency option: The spot exchange rate, the market level of option volatility, the foreign interest rate, the domestic interest rate, and the time to expiration. One way to get a fast look at how these factors work is to examine the change in an option's value when each factor by itself is subject to a small change. Exhibit 4.1 does this experiment on the one-month dollar put/yen call from Chapter 3. Under the base-case assumptions, this option is worth $27,389. When the pricing factors change, the dynamics are as follows:
- A one-yen move in the spot exchange up from 90 to 91 removes $5,234 of value from the option.
- One day of time decay costs the holder of the option $190 as the time to expiration shrinks from 90 days to 89 days.
- A one percent increase in market option volatility, meaning a rise from 14 percent to 15 percent, adds $1,955 to the value of the option.
- An increase in the foreign interest rate by 1 percent, from 2 percent to 3 percent, subtracts $1,233 from the option value.
- An increase in the domestic interest rate by 1 percent, from 5 percent to 6 percent, adds $1,200 to the value of the option.