Analytical Pricing of Floating-Strike European Lookback Options
Summary
The document presents closed-form pricing for floating-strike European lookback calls and puts under Black–Scholes assumptions. A call’s payoff depends on the asset’s terminal value relative to its minimum over the option’s life; a put uses the maximum. The formulas use spot, the relevant path extreme, the risk-free rate, volatility, maturity, and the standard normal cumulative distribution function. The article translates these formulas into C++, including helper functions for intermediate terms and an approximation to the normal CDF.
A numerical example reports call and put prices using a stated spot, observed minimum and maximum, rate, volatility, and one-year maturity. The method assumes a continuously compounded positive risk-free rate and constant volatility, and it relies on the Black–Scholes framework. The article focuses on implementation rather than deriving the theory, refers readers to a mathematical finance text for that derivation, and previews Monte Carlo pricing as a later alternative. Its example does not assess approximation error or discuss market frictions.
Key ideas
- A floating-strike lookback option’s payoff depends on the path’s minimum or maximum as well as the terminal asset price.
- The document gives analytic formulas for European lookback calls and puts under Black–Scholes assumptions.
- The implementation computes intermediate formula terms and approximates the standard normal cumulative distribution function.
- The example prices both option types with specified inputs, but it does not quantify numerical approximation error.
- Constant volatility and a continuously compounded positive risk-free rate are assumed.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.