Question

Calculate the upper and lower bounds respectively for a 9-month European call option on a non-dividend paying share when the share price is R120, the strike price is R125 and the risk-free rate of interest is 8% per annum.

Answer 1

Answer,

theoretical minimum bound of call=Spot price-PV of the strike price

a theoretical maximum bound of call=Spot price

Let us assume that interest is continuous compounding

GIven Information

t=9/12

Spot price(S)=120

Strike price(X)=125

rf=8%/annum

Step 1-PV of strike price

PV of X=125*e^(-8%*9/12)

125*e^0.06

e^0.06=1.0618

e^-0.06=1/1.0618

PV of X=125*1/1.0618=117.724

Answer

theoretical minimum bound of call=Spot price-PV of the strike price

=120-117.724=2.276

theoretical maximum bound of call=Spot price

=120

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