11 Black Scholes Pricing Extension Of No Arbitrage Pricing Requires Market For Underlying Security Risk Priced In Underlying Market Stock Price Distribution –Assume Continuous % Change Distribution –Result Is Lognormal Stock Price Distribution Option Price = f[Stock Price] Dividends Make A Hash Of Math
12 Insurance Pricing Actuarial Estimation Of Expected Loss Principal Use Of Distributions –Per Occurrence Excess Expected Loss –Aggregate Excess Expected Loss –Prove Risk Transfer Risk Premium From The Insurance Market Pure Supply And Demand At Any Time Black/Scholes Has No Practical Use
13 Waceks Paper Black Scholes Discussion Product Design By Analogy
14 Waceks Black Scholes Discussion Observes –Lognormal Stock Price –Option Price = Discounted Excess Pure Premium –Suggests That Risk Premium Is Missing Problems With Footnotes 1 and 2 –1. Price or Premium Does Not Include Risk? –2. Risk Neutral And No Arbitrage Pricing Are The Same?
15 Waceks Bull Cylinder Reinsurance Cylinder –Bull: Long A Call, Short A Put –Bear: Long A Put, Short A Call –If K P < S < K C at expiration either position is worthless. Insurance Companies Are Short The Losses –As Losses Go Up, Insurance Profits Go Down Bull Cylinder Reinsurance –Small (Or Zero) Initial Premium –Low Losses Leave Put In The Money Insurer Pays Additional Premium –High Losses Leave Call In The Money Insurer Recovers From Reinsurer –Retrospective Rating Backwards
16 Waceks Reinsurance Call Options Reinsurance Is A Security Insurers Want To Price Stability Reinsurers Could Offer Call Option –Embedded In Reinsurance Contract –Sold Seperately –Catastrophe Example: 1.46% For Call At 30% With Current Price of 20% Result Is Current Expense Of 21.46% Multi-Year Pricing As Form Of Reinsurance Call
17 Mildenhalls Review Black Scholes Sets Price Including Risk Works Out No Arbitrage For Binomial Case Shows That Actual Price Follows Model