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Monte-Carlo Based Pricing of American Options Using Known Characteristics of the Expected Continuation Value Function

Ottander, Olle LU and Lindstedt, Fredrik LU (2022) In Master's Theses in Mathematical Sciences FMSM01 20221
Mathematical Statistics
Abstract
The problem of pricing American stock options is far more complex than pricing European options due to the possibility of early execution. This feature means that the decision to either hold on to the option or exercising it early must be continually evaluated, leading to closed form solutions such as the Black-Scholes Formula to not be applicable on American options written on dividend paying assets. In 2001, F. Longstaff and E. Schwartz developed a Monte Carlo-based pricing algorithm to handle this. The algorithm simulates a large number of stock price trajectories, evaluates the value of early exercise versus the expected value of holding on to the option using polynomial regression of the continuation value function at each time step... (More)
The problem of pricing American stock options is far more complex than pricing European options due to the possibility of early execution. This feature means that the decision to either hold on to the option or exercising it early must be continually evaluated, leading to closed form solutions such as the Black-Scholes Formula to not be applicable on American options written on dividend paying assets. In 2001, F. Longstaff and E. Schwartz developed a Monte Carlo-based pricing algorithm to handle this. The algorithm simulates a large number of stock price trajectories, evaluates the value of early exercise versus the expected value of holding on to the option using polynomial regression of the continuation value function at each time step and then values the option based on the optimal exercise times. However, this method does not utilize some known characteristics of the expected continuation value function such as convexity, non-negativity, an absolute value of its derivative not greater than 1, and decreasing or increasing depending on the option type. The aim of this thesis is to utilize these characteristics in the regression of the expected continuation value. Four different stock dynamic models are used to simulate the stock price trajectories - Black-Scholes, Merton Jump Diffusion, Finite Moment Log Stable and Heston dynamics. The model parameters are fitted to the market using non-linear least squares optimization. The pricing algorithm resulted in somewhat improved results, with estimates placed within the bid-ask spreads 39.2% of the time using the constraints compared to 35.8% without. The Finite Moment Log Stable stock dynamics performed best with an overall pricing accuracy of 54.9%. Finally, put options were overall more accurately priced than calls, possibly due to constant deterministic interest rates and computational complexities. (Less)
Please use this url to cite or link to this publication:
author
Ottander, Olle LU and Lindstedt, Fredrik LU
supervisor
organization
course
FMSM01 20221
year
type
H2 - Master's Degree (Two Years)
subject
keywords
Option, American Option, Monte-Carlo, Least-Square, Black-Scholes, Merton, Finite Moment Log Stable, FMLS, Heston, Expected Continuation Value
publication/series
Master's Theses in Mathematical Sciences
report number
LUTFMS-3445-2022
ISSN
1404-6342
other publication id
2022:E41
language
English
id
9092655
date added to LUP
2022-06-27 10:14:53
date last changed
2022-06-30 13:57:59
@misc{9092655,
  abstract     = {{The problem of pricing American stock options is far more complex than pricing European options due to the possibility of early execution. This feature means that the decision to either hold on to the option or exercising it early must be continually evaluated, leading to closed form solutions such as the Black-Scholes Formula to not be applicable on American options written on dividend paying assets. In 2001, F. Longstaff and E. Schwartz developed a Monte Carlo-based pricing algorithm to handle this. The algorithm simulates a large number of stock price trajectories, evaluates the value of early exercise versus the expected value of holding on to the option using polynomial regression of the continuation value function at each time step and then values the option based on the optimal exercise times. However, this method does not utilize some known characteristics of the expected continuation value function such as convexity, non-negativity, an absolute value of its derivative not greater than 1, and decreasing or increasing depending on the option type. The aim of this thesis is to utilize these characteristics in the regression of the expected continuation value. Four different stock dynamic models are used to simulate the stock price trajectories - Black-Scholes, Merton Jump Diffusion, Finite Moment Log Stable and Heston dynamics. The model parameters are fitted to the market using non-linear least squares optimization. The pricing algorithm resulted in somewhat improved results, with estimates placed within the bid-ask spreads 39.2% of the time using the constraints compared to 35.8% without. The Finite Moment Log Stable stock dynamics performed best with an overall pricing accuracy of 54.9%. Finally, put options were overall more accurately priced than calls, possibly due to constant deterministic interest rates and computational complexities.}},
  author       = {{Ottander, Olle and Lindstedt, Fredrik}},
  issn         = {{1404-6342}},
  language     = {{eng}},
  note         = {{Student Paper}},
  series       = {{Master's Theses in Mathematical Sciences}},
  title        = {{Monte-Carlo Based Pricing of American Options Using Known Characteristics of the Expected Continuation Value Function}},
  year         = {{2022}},
}