Application of the Option Market Paradigm to the Solution of Insurance Problems [Discussion]

Michael Wacek’s paper is based on the well-known fact that the Black–Scholes call option price is the discounted expected excess value of a certain lognormal random variable.1 Specifically, the Black–Scholes price can be written as (formula), where r is the risk-free rate of interest, T is the time when the option expires, t is the current time, ˜ S(T) is a lognormal random variable related to the stock price S(T)at timeT, k is the exercise price, and x + := max(x, 0). In insurance terms, (L ! k) + represents the indemnity payment on a policy with a loss of L and a deductible k. The Black–Scholes price can also be regarded as the discounted insurance charge (see Gillam and Snader [18] or Lee [25]).