Mathematical analysis of pricing of lookback performance options

Lookback N-time period performance options are proposed. Explicit risk-neutral probability density functions for extrema of N-time period return rates are obtained over the time interval [0, T ], T ≤⃒ 2N. Pricing formulae at t = 0 for lookback performance options with logarithm return rate are derived. The pricing formulae for lookback performance options with gross return rate at t = 0 can be derived similarly. Put-call parity relations at t = 0 for these options follow from these pricing formulae. Applications of lookback performance options are also discussed.

Keywords:

• Lookback Performance Options
• Put Option
• Call Option
• Brownian Motion
• Density Function
• Error Function
• 1991 Mathematics Subject Classifications: 91b28
• 90a12