Forward versus spot modeling
It is possible to base an equity derivatives pricing model on a stochastic driving process for the share price (spot), or for the equity forward. While the former is the classical approach pioneered by Black, Scholes (1973), the latter approach allows to circumvent cost-of-carry modeling for the stock, probably the first and most prominent example of this technique being Black (1976). While the Black-Scholes spot price approach and Black’s forward approach are equivalent, the present note demonstrates that the introduction of local volatility and/or level-dependent default intensity into the driving process destroys this equivalence. The advantages and disadvantages of both approaches are discussed.