Download presentation

Presentation is loading. Please wait.

Published byDion Peat Modified over 4 years ago

1
Bounding Option Prices Using Semidefinite Programming S ACHIN J AYASWAL Department of Management Sciences University of Waterloo, Canada Project work for MSCI 700 Fall 2007 Semidefinite Programming: Models, Algorithms & Computation Course Instructor DR. M. F. ANJOS

2
Introduction 2 Call Option: An agreement that gives the holder the right to buy the underlying by a certain date for a certain price. European vs. American call option

3
Definitions 3 T: Specific time when the underlying can be purchased (Maturity) K: Specific price at which the underlying can be purchased (Strike Price) S t : Price of the underlying (stock) at time t r: Risk-free interest rate α: Expected return on the underlying σ: Volatility in the price of the underlying C: Price of call option

4
Call Option Payoff 4

5
Call Option Pricing 5 Call Option Pricing – An interesting and a challenging problem in finance Black-Scholes (1973) – Asset price follows geometric Brownian motion Stock prices observed in the market often do not satisfy this assumption Can we price the option without assuming any specific distribution for stock price?

6
Bounds on Option Price 6

7
Dual Problems 7

8
Propositions 8

9
SDP Formulation: Upper Bound 9

10
SDP Formulation: Lower Bound 10

11
Comparison with Black-Scholes 11 Black-Scholes assume stock prices follow geometric Brownian motion where N(·) is the cumulative distribution of a normally distributed random variable

12
Computational Experiments 12

13
Computational Experiments 13

14
Computational Experiments 14

15
Computational Experiments 15

16
Computational Experiments 16

17
Cutting Plane Method for Solving[UB_SDP] 17 Let (1) Observations: where represents the polyhedral set corresponding to the linear constraints of Adding constraint (1) tightens the bound. Relaxing SDP constraint on X, Z makes the problems LP

18
Cutting Plane Algorithm 18

19
Performance of the Cutting Plane Algorithm 19 Number of cuts required by the algorithm

20
Conclusions 20 The SDPs produce good bounds on the option price in absence of the known distribution of the stock price. The approach may be used in pricing complex financial derivatives for which closed-form formula is not possible (Boyle and Lin, 1997).

21
21

Similar presentations

Presentation is loading. Please wait....

OK

Options An Introduction to Derivative Securities.

Options An Introduction to Derivative Securities.

© 2018 SlidePlayer.com Inc.

All rights reserved.

To ensure the functioning of the site, we use **cookies**. We share information about your activities on the site with our partners and Google partners: social networks and companies engaged in advertising and web analytics. For more information, see the Privacy Policy and Google Privacy & Terms.
Your consent to our cookies if you continue to use this website.

Ads by Google

Ppt on unity in diversity studio Ppt on set top box Ppt on producers consumers and decomposers worksheets Ppt on power line communication wiki Ppt on tamper resistant packaging Ppt on forward contract examples Ppt on polynomials and coordinate geometry definition Ppt on nature and human beings By appt only movie site Ppt on creativity and innovation management concept