Question

Valuing a European put: Suppose the current price of TIR is DKK 50 per share. In each of the next two years, the stock price will either increase by 20% or decrease by 10%. The 3% one-year risk-free rate of interest will remain constant. Calculate the price of a two-year European call option on TIR with strike price DKK 60.

Answer 1

A. Calculation of the price of a two-year European call option on TIR with strike price DKK 60 using Binomial Model :

• Value of stock after 2 years with 20% increase each year (HP) = DKK 72
• Value of stock after 2 years with 10% decrease each year (LP) = DKK 40.50
• Risk Free rate (r) = 3%
• Strike Price (X) = DKK 60
• Current Market Price (CMP) = DKK 50
• Time = 2years

Therefore,

1.Value of Put Option at high price = Max [{X-HP},0]

=Max [{60-72},0] = 0

2.Value of Put Option at low price = Max [{X-LP},0]

=Max [{60-40.5},0] = 19.5

Calculation of Probability(p) of High Price and Low Price :

• Probability of High Price = CMP*(1+r)t-LP/HP-LP

= 50*(1+0.03)2-40.50/72-40.5

=0.40

• Probability of Low Price = 1-Probability of HP

= 1-0.40 = 0.60

Calculation of expected value as on expiry by using probability :

• Value at HP*p(HP)+Value at LP*p(LP)

=0*0.40+19.5*0.6

=11.7

Calculation of value as on today :

• expected value as on expiry/(1+r)t

=11.7/(1+0.03)2

=DKK 11.03