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DISCUSSION PAPER PI-0713

Options on Normal Underlyings

Paul Dawson, David Blake, Andrew J.G. Cairns and Kevin Dowd

The seminal option pricing work of Black and Scholes [1973] and Merton [1973] was
predicated on the price of the underlying asset being lognormally distributed. Ever since it
became clear that a geometric Brownian motion process provides a more plausible model of
asset prices than its arithmetic equivalent, it has been assumed that an option pricing model
for a normally distributed underlying asset was redundant. Nevertheless, 34 years after Black
and Scholes [1973] and Merton [1973], we identify a contemporary need for such a model:
namely when we wish to price an option on a survivor swap. In this case, an option-pricing
model based on a normal underlying is not some flawed relative of Black-Scholes, as it is
usually considered to be, but is instead the key to pricing this type of swaption correctly – and
hence, a very useful tool in the rapidly emerging universe of survivor derivatives. Accordingly,
this paper derives the call and put valuation models for options on normal underlying assets,
and derives their Greeks. It then shows how this option pricing model can be used to price
swaptions on survivor swaps.