Pricing American Put Options Using Malliavin Calculus with Optimal Localization Function

2021 ◽  
Author(s):  
Mohamed Kharrat
Keyword(s):  
Malliavin Calculus ◽  
Put Options ◽  
Localization Function ◽  
American Put Options ◽  
American Put ◽  
Optimal Localization

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.

An Early-Exercise-Probability Perspective of American Put Options in the Low-Interest-Rate Era

2014 ◽  
Vol 35 (12) ◽  
pp. 1154-1172 ◽  
Author(s):  
Daniel Wei-Chung Miao ◽  
Yung-Hsin Lee ◽  
Wan-Ling Chao
Keyword(s):  
Interest Rate ◽  
Put Options ◽  
Early Exercise ◽  
American Put Options ◽  
American Put

Robust upper bounds for American put options

2018 ◽  
Vol 39 (1) ◽  
pp. 3-14
Author(s):  
Ye Du ◽  
Shan Xue ◽  
Yanchu Liu
Keyword(s):  
Upper Bounds ◽  
Put Options ◽  
American Put Options ◽  
American Put

scholarly journals OLD PROBLEMS, CLASSICAL METHODS, NEW SOLUTIONS

2020 ◽  
Vol 23 (04) ◽  
pp. 2050024
Author(s):  
ALEXANDER LIPTON
Keyword(s):  
Classical Method ◽  
Mean Field ◽  
Trading Strategies ◽  
Financial Mathematics ◽  
Uhlenbeck Process ◽  
Put Options ◽  
Default Intensity ◽  
American Put Options ◽  
The Mean ◽  
American Put

We use a powerful extension of the classical method of heat potentials, recently developed by the present author and his collaborators, to solve several significant problems of financial mathematics. We consider the following problems in detail: (a) calibrating the default boundary in the structural default framework to a constant default intensity; (b) calculating default probability for a representative bank in the mean-field framework; and (c) finding the hitting time probability density of an Ornstein–Uhlenbeck process. Several other problems, including pricing American put options and finding optimal mean-reverting trading strategies, are mentioned in passing. Besides, two nonfinancial applications — the supercooled Stefan problem and the integrate-and-fire neuroscience problem — are briefly discussed as well.

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