Basket Option (Levy Approximation)
Computes the price of a call on a basket of two assets with the Levy approximation. The weighted sum of two lognormal assets isn't lognormal, so there's no exact formula; Levy matches the basket's mean and variance to an equivalent lognormal and applies a Black-Scholes. It's the practical way to price options on indices and portfolios, where the correlation between assets is decisive. Enter the two prices, the weights, the strike, the volatilities, the correlation, the rate and the term.
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Basket Option (Levy Approximation)
Computes the price of a call on a basket of two assets with the Levy approximation. The weighted sum of two lognormal assets isn't lognormal, so there's no exact formula; Levy matches the basket's mean and variance to an equivalent lognormal and applies a Black-Scholes. It's the practical way to price options on indices and portfolios, where the correlation between assets is decisive. Enter the two prices, the weights, the strike, the volatilities, the correlation, the rate and the term.
An option on several assets at once
Funds and indices aren't a single asset but a basket of them. Pricing an option on that basket hits a mathematical snag: the sum of lognormal assets isn't lognormal, so Black-Scholes doesn't apply directly. An approximation is needed, and Edmond Levy's, from 1992, is one of the most used.
The idea is the same as Turnbull-Wakeman for Asians: match moments. Levy computes the exact mean and variance of the basket's value at expiry and pretends it's lognormal with those two moments, then applies a Black-Scholes with the resulting effective volatility. The correlation between the assets enters directly into that variance, and it's what moves the price most.
Enter the two asset prices, their weights in the basket, the strike, the volatilities, the correlation, the interest rate and the term. The tool returns the basket call premium. The lower the correlation, the more diversification reduces the basket's volatility and, therefore, the option's price.
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The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.