Options on normal underlyings with an application to the pricing of survivor swaptions

Abstract

Survivor derivatives are gaining considerable attention in both the academic and practitioner communities. Early trading in such products has generally been confined to products with linear payoffs, both funded (bonds) and unfunded (swaps). History suggests that successful linear payoff derivatives are frequently followed by the development of option-based products. The random variable in the survivor swap pricing methodology developed by Dowd et al [2006] is (approximately) normally, rather than lognormally, distributed and thus a survivor swaption calls for an option pricing model in which the former distribution is incorporated. We derive such a model here, together with the Greeks and present a discussion of its application to the pricing of survivor swaptions.

Survivor Derivatives: A Consistent Pricing Framework

“…Our survivor swaptions are specified on the swap premium π as the underlying, and this raises the issue of how π is distributed. In a companion paper, Dawson et al (2009) suggest that π should be (at least approximately) normal, and they report Monte Carlo results that support this claim 14 . We can therefore state that π is approximately N (π forwardswap , σ 2 ), where σ 2 is expressed in annual terms in accordance with convention.…”

“…Dawson et al (2009) derive and test a model for pricing options on assets with normally distributed prices and application of their model to survivor swaptions gives the following formulae for the swaption prices: …”

“…We show that this approach can be used to price a range of other linear survivor derivatives. The second component is the application of the option‐pricing model set out by Dawson et al (2009) to the pricing of survivor options such as survivor swaptions. This is a very simple model based on a normally distributed underlying, and it can be applied to survivor options in which the underlying is the swap premium or price, since the latter is approximately normal.…”

“…The “” section then uses this framework to price a range of other linear survivor derivatives: these include survivor forwards, forward survivor swaps, survivor basis swaps, and survivor futures contracts. The “” section extends the pricing framework to price survivor swaptions, caps, and floors, making use of an option pricing formula set out in Dawson et al (2009). The “” section gives a number of hedging applications of our pricing framework, and the “” section concludes.…”

“…This article applies the approach developed by Dowd et al (2006), Olivier and Jeffery (2004), Smith (2005), and Cairns (2007) to derive a consistent framework for pricing a wide range of linear survivor derivatives, such as forwards, basis swaps, forward swaps, and futures. It then shows how a recent option pricing model set out by Dawson et al (2009) can be used to price nonlinear survivor derivatives, such as survivor swaptions, caps, floors, and combined option products. It concludes by considering applications of these products to a pension fund that wishes to hedge its survivorship risks.…”