Option Pricing
Inputs
To price an option, we need a number of inputs:
• Spot price
• Forward discount or premium (or foreign and domestic interest rates)
• Cost of carry (the “domestic” rate)
• Whether the option is a call or a put
• Whether the option is a European or an American style option
• The expiration date of the option
• The implied volatility
When we analyze the above list of inputs, we notice that:
• Spot, forwards and interest rates are parameters determined by other market
• The call, put, European, American and expiration date parameters are all part of the option contract and remain fixed for the life of the option
The only parameter over which the option trader has an influence is the volatility
Making markets in options is equivalent to making markets in volatility. Because the foreign exchange market is so liquid and transparent, inter-bank option trading is done exclusively on a volatility basis. Two traders will agree on the volatility at which they wish to trade a particular option, and subsequently agree on all the other market parameters. The option contract parameters are given.
Note
• Volatility quoting is not necessarily applicable to exotic options trading.
• Even though six of the seven parameters are given, the trader still needs to make sure that all of the inputs are correct!
For a “naked” option position, usually the most significant risk is the movement of the (spot) price of the underlying instrument. This is followed by the volatility risk and by the time decay. Finally, interest rate movements will also affect the valuation of an option, by changing the forward price and by changing the discounting of the premium.
In option trading, all of these risks are measured and have specific names.
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