Swing Option Pricing by Dynamic Programming with B-spline Density Projection

2019 ◽  
Author(s):  
Justin Kirkby ◽  
Shijie Deng
Keyword(s):  
Dynamic Programming ◽  
Option Pricing ◽  
B Spline ◽  
Swing Option

DISTRIBUTION-BASED OPTION PRICING ON LATTICE ASSET DYNAMICS MODELS

2002 ◽  
Vol 05 (06) ◽  
pp. 599-618 ◽  
Author(s):  
YUJI YAMADA ◽  
JAMES A. PRIMBS
Keyword(s):  
Dynamic Programming ◽  
Option Pricing ◽  
Network Flow ◽  
Stock Price ◽  
Implied Volatility ◽  
Market Model ◽  
Flow Optimization ◽  
Optimal Hedging ◽  
Hedging Problem ◽  
Network Flow Optimization

In this paper, we propose a numerical option pricing method based on an arbitrarily given stock distribution. We first formulate a European call option pricing problem as an optimal hedging problem by using a lattice based incomplete market model. A dynamic programming technique is then applied to solve the mean square optimal hedging problem for the discrete time multi-period case by assigning suitable probabilities on the lattice, where the underlying stock price distribution is derived directly from empirical stock price data which may possess "heavy tails". We show that these probabilities are obtained from a network flow optimization which can be solved efficiently by quadratic programming. A computational complexity analysis demonstrates that the number of iterations for dynamic programming and the number of parameters in the network flow optimization are both of square order with respect to the number of periods. Numerical experiments illustrate that our methodology generates the implied volatility smile.

SWING OPTION PRICING BY DYNAMIC PROGRAMMING WITH B-SPLINE DENSITY PROJECTION

2019 ◽  
Vol 22 (08) ◽  
pp. 1950038
Author(s):  
J. LARS KIRKBY ◽  
SHI-JIE DENG
Keyword(s):  
Dynamic Programming ◽  
Cash Flows ◽  
General Purpose ◽  
Future Research ◽  
Unified Framework ◽  
Swing Options ◽  
Early Exercise ◽  
Swing Option ◽  
Financial Derivative ◽  
Exponential Lévy Models

Swing options are a type of exotic financial derivative which generalize American options to allow for multiple early-exercise actions during the contract period. These contracts are widely traded in commodity and energy markets, but are often difficult to value using standard techniques due to their complexity and strong path-dependency. There are numerous interesting varieties of swing options, which differ in terms of their intermediate cash flows, and the constraints (both local and global) which they impose on early-exercise (swing) decisions. We introduce an efficient and general purpose transform-based method for pricing discrete and continuously monitored swing options under exponential Lévy models, which applies to contracts with fixed rights clauses, as well as recovery time delays between exercise. The approach combines dynamic programming with an efficient method for calculating the continuation value between monitoring dates, and applies generally to multiple early-exercise contracts, providing a unified framework for pricing a large class of exotic derivatives. Efficiency and accuracy of the method are supported by a series of numerical experiments which further provide benchmark prices for future research.

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