Approximating equity volatility
The volatility estimation is a crucial problem for pricing derivatives. The traditional implied volatility approach induces the undesired smile effect and is therefore inconsistent with the market reality. A second more realistic approach is due to Bensoussan, Crouhy and Galai (1995) who derive an extension of the Black-Scholes model where the stochastic volatility ?is endogenous and depends on the change in the firm’s financial leverage. These authors give an analytic approximation for ?when the firm is financed by external funds such as debts, under the assumptions that the risk-free rate and the volatility of the return on the firm’s asset are constant. In this work, we will generalize this result by allowing these parameters to be variable.
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