Risk Management Homework

Short answers (2-points each)

  1. When E -S < 0 a put option is said to be
  2. The Put-Call Parity points to a mispricing. The Fiduciary Call value is greater than the value of the Protective Put. To take advantage of the arbitrage opportunity you should sell the and buy the
  3. When S > E the Call option is said to be
  4. Applying the Put-Call Parity relationship, create a synthetic Call

Problems:

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  1. Tabulate the value at expiration for each of the following portfolios. Grapheach value andPayoff function. Be sure to label breakeven points. All options are European, written on the same stock, with the same expiration date.
  1. Long put E = 55, P55=$3.25, two Short Puts E = , P60 = $7, long put E=65 P65 = $10 (10-pts.)
  1. A straddle is a long Call E=$35 C35=$2.50 and a long Put E = $35 P35=$1.75 (10-pts)
  2. A stock is trading for $63 per share. A 3-month (90-day) call and put options are written on the stock with an exercise price of $60 are trading for $6.00 and $2 respectively.
  1. Create a 90- day Synthetic Investment. (8-points)
  1. Calculate your return on investment (the implied RF in the prevailing prices). ( 8-points)
  2. A stock is trading for $172. A July Put and Call expiring in 50 days with an exercise price E=$175 are trading on the stock. The 50-day Risk Free Rate is 2.0% , the Call Premium,

C=$ 6.0 and the Put price, P= $5.50

  1. Applying the Put Call parity, does an arbitrage opportunity exist? If so, how would you take advantage of the mispricing? (10-points)
  1. Calculate the arbitrage profit. (10-points)
  1. A stock is currently trading at $82. The stock volatility as expressed by its standard deviation is 18%. A Call with an exercise price of $80 is expiring in 90 days. The 3-month treasury is selling to yield 2%.

All options are European, written on the same stock, with the same expiration date. (36- points)

  1. Create a 3- period binomial lattice. Provide the Call values at each node. For the first and second periods, calculate the time value of the option at each node.
  1. What should be the fair value of the Call option today?
  1. Given the fair value of the Call option, calculate the fair value of the Put option today.

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