Question

1. J-Rata Corp shares are currently trading at $30 each. It is expected to increase by 10% or decrease by 6% during the next two-three months. If its strike price at maturity in six months is set as $32 and the risk free rate is 8% per annum for all maturities:

1. calculate its call options price and its put option price currently.

2. Test and prove that the put-call parity is holding based on your option pricing.

Answer 1

Value of Call Option at Expiry = Maximum of (Stock price - Strike Price) or 0

Value of Call Option at Node = [(Probability of Up Move)*(Value of option at the upper node) + (Probability of Down Move)*(value of option at the lower mode)]/e^{(-rf*dT​​​​)​​​}
where dT = time between 2 periods

Probability of Up Move = [e^(-rf*dT) - Down Move] / [Up Move - Down Move]
Probability of Down Move = [1 - Probability of Up Move]

Value of Call Option = $1.04

Value of Put Option = $1.79

Value of Put Option at Expiry = Maximum of (Strike price - Stock Price) or 0

Value of Put Option at Node = [(Probability of Up Move)*(Value of option at the upper node) + (Probability of Down Move)*(value of option at the lower mode)]/e^(-rf*dT​)​​​​​​
where dT = time between 2 periods

Probability of Up Move = [e^(-rf*dT)​​​​​​​ - Down Move] / [Up Move - Down Move]
Probability of Down Move = [1 - Probability of Up Move]

Put-Call Parity

It has 2 portfolios.
Portfolio 1 = Long Stocks + Long Put Option
Portfolio 2 = Long Call Option + PV of Zero Coupon Bond of the same maturity as options

Stock + Put Option = Call Option + Strike Price * e^{-r * t}

30 + 1.79 = 1.04 + 32 * e^{-0.08 * 0.5}

31.79 = 1.04 + 30.74526205

31.79 = 31.78526205 ~ 31.79

Hence, the put-call parity holds