**FINA4350 HW 5. Due: TH FEB 28 ****p. 1/2 **

**From the textbook study Sections: 13.5, 13.7, 13.9, 13.10 and 13.11
All the annual rates in the book are with continuous compounding.**

**13.13.** **What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is three months?**Given: , , , , and .

European call price is:

**13.14.** **What is the price of a European put option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is six months?**Given: , , , , and .

European put price is:

**Q3.Calculate the Black-Scholes-Merton premiums of at-the money call and put on a non-dividend paying stock. St = 40 and σ = 50%. Suppose that the yields on the T-bill that matures 143 from the date the table is given are Ra = 4.50% and Rb = 4.60%. These are annual rates with a single compounding period. Remember that this means that the options mature in 144 days. **

=.04655

__For Q4 – Q8 use the table below.__

**Q4.Suppose that the table below presents prices of European options and that the underlying stock does not pay dividends. Open an arbitrage profit making Calendar spread with the K=30, APR and JUL puts. Using a table of cash flows and P/L at expiration, demonstrate that this strategy is indeed an arbitrage profit making strategy. **

**Q5.1 Suppose that the table below presents prices of European options and that the underlying stock does not pay dividends. Check numerically whether or not the put call parity holds for the K=25, JUL options. JUL expiration is in 144 days. The annual risk-free rate that applies for JUL expiration is 4.52%. **

**Q5.2 If the parity does not hold, create a strategy that will yield an arbitrage profit and, using a table of CFs and P/L at JUL expiration, calculate the arbitrage profit per share. **

**p.2/2 **

**Q6. Calculate the Black-Scholes-Merton prices for the call and the put of the K = 40; T – t = 144/365yrs; the risk-free annual rate with one compounding period R1 = 4.52% and VOL≡ σ = 53.70%. **

**Q7.Consider two European call options with two different strike prices denoted by: K1 < K2. Both calls are on the same non dividend paying stock and for the same expiration date, T. It is known that the premiums on these calls satisfy the following inequality: **

**Atanytime t, (t<T), c(K1)–c(K2)≤(K2 –K1)e–r(T–t) **

**7.1 Given that the annual risk-free rate is r = 4.52% and that the JUL time to expiration is 144 days, check numerically whether this result holds for the K1 =30andK2 =35JULcalls. **

**7.2 If the result does not hold, open a strategy that will create an arbitrage profit and, using a table of cash flows and P/L at JUL expiration, calculate the arbitrage profit per share. **

**Q8.**

**Suppose that the table below refers to American options and that the quotes in the table are given an instant before the stock goes x- dividend. The dividend (an instant later) will be in the amount of $.75/share.
Indicate which calls will be exercised this instant. Explain why.**

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S |
K |
Call |
Call |
Call |
Put |
Put |
Put |

MAR |
APR |
JUL |
MAR |
APR |
JUL |
||

29.50 |
25.00 |
4.88 |
5.30 |
7.29 |
.44 |
.75 |
1.85 |

29.50 |
27.50 |
2.63 |
3.63 |
– |
1.00 |
1.94 |
– |

29.50 |
30 |
1.56 |
2.44 |
6.29 |
2.00 |
3.00 |
2.75 |

29.50 |
32.50 |
.53 |
1.83 |
– |
3.50 |
4.50 |
– |

29.50 |
35 |
.31 |
.81 |
1.33 |
5.75 |
6.25 |
7.38 |

29.50 |
37.50 |
– |
.50 |
– |
– |
9.00 |
– |

29.50 |
40 |
.08 |
.31 |
1.25 |
10.50 |
10.87 |
11.06 |