Introducing Option Pricing
• Binomial Pricing in discrete times
• Transition to Continuous time BSOPM
Simple Heuristics on the
Black-Scholes Option
Pricing Model
Rossitsa Yalamova
University of Lethbridge
Objective and Goal
• Develop passion for creative solution and
intuition of the variables relationships in the
model
• Develop instructional design and educational
technology for the foundations of derivative
valuation and the basic principles of risk
management and hedging.
Problem Solving
• Algorithms do not necessarily lead to
comprehension but promise a solution,
while heuristics are understood but do not
always guarantee solutions.
• PDE for the solution of the BSOPM
Visualization heuristics
• Graphs, drawings and other visualization
tools meet specific learning needs.
Discounted Cash flow Valuation
• European option pays only at expiration=S-K
Log Returns and call intrinsic value
• Continuous Compounding/Discounting
• Discrete vs. Continuous return
Review of Probability and
Return Calculations
• Lognormal prices
• Return Probability calculations
Stock price at expiration?
• Crystal bowl or probability
The Black-Scholes model:
 rt
C  SN (d1 )  Ke N (d 2 )
where
d1 
2


S

 
t
ln     r 
2 
K 
 t
and
d 2  d1   t
Concrete example technique
• Option at the money (S=K) risk free rate is 0:
Option at the money (S=K); R=0
(S=K); risk free rate positive
• Risk free rate moves the area to the right by
and increases the value as K is discounted
Adding positive instantaneous return (S>K)
• The
moves to the right by
Option “out-of-the-money”; r=0
• The area
moves to the left by
Option “out-of-the-money”; r>0