**I. Binomial Pricing**

1.Using a non-arbitrage argument price a put option with strike $**80** on a stock that sells for **$70** and will be selling for either $85 or $75 in one year. The risk-free rate is 10%.

**II.BSOPM** : (construct (graphically)

S | 35 |

T | 73 days |

K | 30 |

sigma | 0.525 |

R | 0.08 |

1.Call =…….…… 2. Put = ………….

2.Delta of the put =………

Delta neutrality ratio #calls……….. and #puts……………….

3. What is the put price if the stock price increases $1?

4.A stock portfolio holds $10 million market value and an average beta=1.45. What is the hedge ratio for removing exposure to market risk if S&P500 Futures are 1,123.5? How many contracts do you need to hedge?

What position should you establish?

If you want to increase exposure to beta 1.8 how many contracts do you need? Determine the type of position:

What is the price of a bond that pays 6% annual coupon and has 4 years to maturity if the term structure is:

S (0-1) | 2.2 |

S (0-2) | 2.6 |

S (0-3) | 3.2 |

S (0-4) | 4.1 |

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