Question

10.To create a delta-neutral portfolio, the SIT fund has sold 10,000 put options on Epsilon stock with a strike price of $80 when the shares were trading at $100. The risk manager from SIT uses the Black-Scholes model to value all its option exposures. The current price of the shares is $90. The annualized standard deviation of Epsilon stock returns is 20%and the option expires in six months. If the risk-free rate is 2%, approximately, what is the likelihood that this option will be exercised?
(a)0.7975
(b)0.5329
(c)0.4241
(d)0.2033

Answer 1

As per Black-Scholes Model, The value of the put is given by:

Where and

where X= Strike Price, S= Current Stock Price, r= Risk-free Rate, = Standard Deviation, T= Time

In this question,

X= $80, S= $90, r=2%, T=6/12=0.5, =20%

so

          = (0.1177 + 0.02) / 0.1414

         = 0.9742

      = (0.1177 + 0)/ 0.1414

      = 0.8322

    = 80 * 0.99* 0.2026 - 90 * 0.1649

    = 16.0467 - 14.8480

    = 1.1986