Transcript presentation.ppt

The Stock Option Pricing problem and
the Conduction Heat Transfer Problem.
Main Features:
•Need to become familiar with the
associated stock option jargon.
•Compare governing equations, analytical
solutions, and constraints.
•What heat conduction problem is satisfied
by the boundary conditions of an option
pricing problem?
Explanation of terms (1)
•Option
•Exercise price
•Asset price
•Expiry
•Call
•Put
•Volatility, risk-free interest rate
Explanation of Terms (2)
Asset Name
Asset Value
Exercise
Prices
Expiry Dates
Call Values
C(S, t)
Put Values
P(S, t)
Governing Equations and Constraints
C ( S , t )  max( S  E ,0)
P ( S , t )  max( E  S ,0)
V 1 2 2  2V
V
  S

rS
 rV  0
2
t 2
S
S
 2T 1 T

0
2
x
 t
Black-Scholes Eq.
1D Heat Conduction
Analytical Solution
C ( S , t )  SN (d1 )  Ee r (T t ) N (d 2 )
P( S , t )  Ee

 r ( T t )
N ( d 2 )  SN ( d1 )
T  x, t    cm X  m , x e
m 1
 m2 t
Solutions for Call & Put
Heat Conduction problem satisfied by optionpricing constraints