In this chapter we describe the pricing of Bermudan options by means of Fourier cosine expansions. We propose a technique to price early-exercise call options with the help of the (European) put-call parity and put–call duality relations. Direct pricing of call options with cosine expansions may give rise to some sensitivity regarding the choice of the size of the domain in which the Fourier ex...

This pa per suggests a simple valuation method based on Chebyshev approximation at Chebyshev nodes to value American put options. It is similar to the approach taken in Sullivan (2000), where the option`s continuation region function is estimated by using a Chebyshev polynomial. However, in contrast to Sullivan (2000), the functional is fitted by using Chebyshev nodes. The suggested method is f...

It is well known [5], [1] that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper investigates such a Call Put duality for perpetual American options. It...

We consider a non necessarily complete financial market with one bond and one risky asset, whose price process is modelled by a suitably integrable, strictly positive, càdlàg process S over [0, T ]. Every option price is defined as the conditional expectation under a given equivalent (true) martingale measure P, the same for all options. We show that every positive contingent claim on S can be ...

We introduce a variant of the classic sealed-bid unit-demand auction in which each item has an associated put option. The put option of an item is held by the seller of the item, and gives the holder the right to sell the item to a specified target bidder at a specified strike price, regardless of market conditions. Unexercised put options expire when the auction terminates. In keeping with the...