Benchmark Models in Continuous Time

The option pricing model developed in a groundbreaking paper by Black and Scholes (1973), formalized and extended in the same year by Merton (1973), enjoys great popularity. It is computationally simple and, like all arbitrage-based derivative pricing models, does not require the knowledge of an investor’s risk preferences. Option valuation within the Black-Scholes framework is based on the already familiar concept of perfect replication of contingent claims. More specifically, we will show that an investor can replicate an option’s return stream by continuously rebalancing a self-financing portfolio involving stocks and risk-free bonds. At any date t, the current wealth of a replicating portfolio determines the arbitrage price of an option.