Portfolio Based Pricing of Residual Basis Risk with Application to the S&P 500 Put Options

Financial option pricing methodology since Black and Scholes (1973) defines option prices as the hedging cost to set up a riskless hedged portfolio. Financial options are treated as redundant contracts, since they can be replicated by trading the underlying assets. The so-called "relative valuation" method prices financial options in the world of the risk-neutral measure. On the actuarial side, there is no liquid secondary market for insurance contracts; thus, insurance and reinsurance contracts are viewed as non-redundant, primary contracts to complete the market. Actuarial risk models that price insurance liability contracts are not based on an assumption of hedging, instead considering the present value of future losses and the cost of allocated.

This paper is devoted to pricing "hybrid" (insurance and financial) risk products by combining the financial option pricing method with the actuarial pricing method. It suggests that the price of contingent claims containing both hedgeable risk and unhedgeable risk should reflect the average cost of hedging, plus a risk premium that compensates for the marginal residual risk the contract brings to the existing portfolio. To evaluate the residual risk, a portfolio-based pricing method is proposed to evaluate loss and systematically consider risk premium. The risk premium is charged to satisfy risk management and return on risk capital requirements. The proposed method is tested by pricing the Standard and Poor's 500 index (SPX) options in a simulated objective world.