Pricing with a smile

In the January 1994 issue of Risk, Bruno Dupire showed how the Black-Scholes model can be extended to make it compatible with observed market volatility smiles, allowing consistent pricing and hedging of exotic options


The Black-Scholes model gives options prices as a function of volatility. If an option price is given by the market we can invert this relationship to get the implied volatility.

If the model were perfect, this implied value would be the same for all option market prices, but reality shows this is not the case. Implied Black-Scholes volatilities strongly depend on the maturity and the strike of the European option under scrutiny. If the implied volatilities of at-the

Only users who have a paid subscription or are part of a corporate subscription are able to print or copy content.

To access these options, along with all other subscription benefits, please contact [email protected] or view our subscription options here:

You are currently unable to copy this content. Please contact [email protected] to find out more.

To continue reading...

You need to sign in to use this feature. If you don’t have a account, please register for a trial.

Sign in
You are currently on corporate access.

To use this feature you will need an individual account. If you have one already please sign in.

Sign in.

Alternatively you can request an individual account here: