ABSTRACT
The net present value of a European vanilla call option is the payoff at option contract expiry discounted to the present date. The discount rate reflects the funding cost, liquidity risk, and credit risk, entities that differ among market participants. This chapter uses the Black–Scholes option pricing formula as the mapping tool to infer the implied volatility and the implied discount rate as the pair of implied parameters of interest from the day-close bid-ask mid-quote prices pertaining to a set of European vanilla call option contracts. It first investigates the sensitivity of implied volatility mapping with respect to the uncertainty in discount rate specification using the construct of an under-defined system of nonlinear equations. The chapter describes a numerical strategy that deploys an algorithm to simultaneously infer implied volatility and implied discount rate from option prices using the construct of an over-defined system of nonlinear equations.
