Project Presentation

1
Project Presentation
Towards a Dependable Framework on Numerical
Approach to Pricing European Options

• Course CS757 Computational Finance
• Presented By David Allenotor (CS757.2003.021)
• Prof Dr. Ruppa K. Thulasiram

2
Presentation Outline

• Introduction
• Background/Motivation
• Method
• Results
• Conclusion

3
Introduction

• What are Options?
• Basic Terminologies
• Option Theory Basic Concepts
• Options Pricing Techniques
• Basic concepts of European Options
• Numerical Analysis of Options
• Basic Numerical Approximation Concepts

4
Background/Motivation

• European Option Pricing equation
• Basic Notations Notations
• B-S Equations for European Options
• Boundary Final conditions for European options
• Analytical solution to the B-S equation
• Numerical Schemes for Approximating European
  Options
• Finite-Difference Method (FDM) for European
  Options
• Binomial Method (BM)

5
Background/Motivation

• Binomial Method
• Finite Difference Method
• 1. Initialize parameters K, T, S, r, N, u, d
  2. Compute the constants dt T/N           p
  ( exp(rdt)-d)/(u-d))           disc exp(-r
  dt) 3. (Initialize asset prices at maturity
  time step N)           St0 SdN          
  for j 1 to N          Do Stj Stj-1u/d
  4. (Initialize option values at maturity)
           for j 0 to N do Cj max( 0.0, Stj
  -K) 5. Step back through the tree          for
  i N-1 downto 0 Do          for j0 to i Do
           Cj disc (pCj1 (1-p) Cj
  )           European Call C0

6
Background/Motivation

• Specific Problem
• The need to Reduce Finance problems from wide to
  narrow region of solution space and its
  subsequent implementation in exact boundary
  condition.

7
Background/Motivation
8
Methodology

• Solution Strategy and Implementation
• Derivation of the BS Eq. For Evaluating European
  Options
• Analysis of Boundary final Condition for
  European Options
• Solution Partitioning
• X(t) 0,MX0,T

9
Experimental Frame Work

• Option Value c(S,t) S-K
• Estimated Option Value
• Estimated error in Computation

10
Experimental Results

• Table 1 Finite Difference Method

11
Experimental Results
Graph 1 Strike Prices Vs. Option Values Finite
Difference Method
12
Experimental Results
Table 2 Binomial Method
13
Experimental Results
Graph 2 Graph of strike Prices Vs. Options
Values Binomial Method
14
Experimental Results
Table 3 Error Estimates
15
Experimental Results
Graph 3 Graph of Strike Prices Vs.
16
Contribution to Knowledge

• Results obtained from our method improves those
  of Binomial and Finite Difference Methods

17
Conclusion Future Work

• There is a non zero difference between FDM and BM
• Fuzzy option pricing will enhance results of
  Numerical Crisp Pricing of Options.

18
References
19
Thank You