What is the theoretical price

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Derivative Securities Assignment

Question 1 -

The S&P 500 spot level is 2,383. The 1-year at-the-money call on is selling at $150. The risk-free rate is 4% and the index pays a dividend yield of 3%. The S&P 500 options are European.

(a) What is the theoretical price of the 1-year at-the-money put price?

(b) The 1-year put is selling at $120 on the market, show how you can benefit from this arbitrage opportunity. Show all details.

Question 2 -

Consider a 6-month bull call spread on MDLZ with strikes of $35 and $50. TSLA spot price is $43 and its volatility is 20%. The risk-free rate is 4% per annum continuously compounded. We assume that MDLZ is not expected to pay any dividend.

(a) Use a 6-step binomial tree to price the spread (note: up and down movements need to match the volatility. Show all the tree parameters).

(b) What are the break-even point(s), the maximum profit and maximum loss for this strategy?

Question 3 -

A European derivative instrument on MDLZ has the following payoff structure at the maturity date in 3 years:

a) S_T if S_T < 30

b) 30 + 2 * (S_T - 30) if 30 < = S_T <= 50

c) 70 if 50 <= S_T <= 70

d) S_T if 70 <= S_T

where S_T is the price at the maturity date. The spot price is 44 and the volatility is 20%. The risk-free interest rate is 4% and we consider a 6-step binomial tree.

(a) Use Excel to draw this payoff pattern for the following price interval [0 , 100] with a step of 5.

(b) Based on the graph in (a), explain briefly how the premium of this derivative security should compare to MDLZ spot price.

(c) Price this contract using a 6-step binomial tree and confirm your findings in (b). Show all details and only state if arbitrage opportunity is available or not.

Question 4 -

Consider a 1-year European put on AMZN with a strike price of $900. AMZN spot price is $850 and its volatility is 20%. AMZN is expected to pay no dividend. The risk-free rate is 4%.

(a) Use Black-Scholes-Merton (BSM) model to price this put option.

(b) What is the put delta? If the short position decides to delta-hedge, what would the net cash flow be?

Question 5 -

We consider the following options strategy on GOOG and its total payoff at the expiry date of the short-term option.

Option	Type	Position	Remaining Life	Strike
1	Call	Short x 1	0	750
2	Call	Long x 2	0.5	800
3	Call	Short x 1	0	850

For the options with a remaining life, we use BSM model to determine their values. We assume a volatility of 30% and a risk-free rate of 4%.

(a) Compute the total payoff for S = 750, 800 and 850.

(b) Use Excel to draw the payoff pattern for prices between $500 and $1000 with a step of $10.

Reference no: EM131468430

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4/20/2017 3:38:04 AM

This assignment is to be done individually. You must sign and submit the standard cover page supplied as the last page of this assignment. Staple your assignment prior to handing it in. The work can be typed or handwritten. If it is handwritten and too difficult to read due to messiness and poor handwriting, it will receive zero credit. You must show your work to receive full credit. This assignment contains 5 questions and carries a total of 30 points.

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