Pricing American Put Options by Fast Solutions of the Linear Complementarity Problem

2002 ◽  
pp. 325-338 ◽  
Author(s):  
Artan Borici ◽  
Hans-Jakob Lüthi
Keyword(s):  
Linear Complementarity Problem ◽  
Complementarity Problem ◽  
Linear Complementarity ◽  
Put Options ◽  
American Put Options ◽  
American Put

scholarly journals Pricing Perpetual American Put Options with Asset-Dependent Discounting

2021 ◽  
Vol 14 (3) ◽  
pp. 130
Author(s):  
Jonas Al-Hadad ◽  
Zbigniew Palmowski
Keyword(s):  
Value Function ◽  
Asset Price ◽  
Stopping Times ◽  
Martingale Measure ◽  
Put Options ◽  
American Put Options ◽  
Exact Calculations ◽  
Negative Exponential ◽  
American Put ◽  
The Value Function

The main objective of this paper is to present an algorithm of pricing perpetual American put options with asset-dependent discounting. The value function of such an instrument can be described as VAPutω(s)=supτ∈TEs[e−∫0τω(Sw)dw(K−Sτ)+], where T is a family of stopping times, ω is a discount function and E is an expectation taken with respect to a martingale measure. Moreover, we assume that the asset price process St is a geometric Lévy process with negative exponential jumps, i.e., St=seζt+σBt−∑i=1NtYi. The asset-dependent discounting is reflected in the ω function, so this approach is a generalisation of the classic case when ω is constant. It turns out that under certain conditions on the ω function, the value function VAPutω(s) is convex and can be represented in a closed form. We provide an option pricing algorithm in this scenario and we present exact calculations for the particular choices of ω such that VAPutω(s) takes a simplified form.

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