ICWO Deriv Mo C Key Stud - Examples for assignment questions PDF

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Mo Chaudhury, Derivatives

IN-CLASS WORKOUT # 1

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IN-CLASS WORKOUT # 2 It is now January 2017. A company anticipates that it will sell 2.00 million barrels of light sweet crude oil in July 2017 and sell 3.00 million barrels in January 2018. NYMEX Light Sweet Crude futures contracts (1 contract is for 1,000 barrels or 42,000 gallons) are available for hedging price risk. Company decided to hedge 70% of its July 2017 exposure and 80% of its January 2018 exposure, and to use at all times futures contracts maturing in less than 10 months.

[Round the number of contracts to the nearest integer]. Under the appropriate strategy for hedging both of its future spot transactions: (a) How many contracts of what position type (LONG or SHORT) and which maturity the company should open now (Jan17)? (e.g., OPEN W# of Contracts of Maturity X,..); (b) What futures trades in Jul17 are planned? (e.g., CLOSE W# of Contracts of Maturity X, and OPEN Y# of Contracts of Maturity Z, ..); (c) Considering all futures positions opened prior to Jul17, what is the ex-post total cumulative gain or loss as of July 2017? (d) What all-in (effective) price/barrel did the company realize ex-post for its Jul17 and Jan18 transactions?

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IN-CLASS WORKOUT # 3 Say, at the end of 2013, Zarrick Gold entered into a commitment to sell 2.0 million ounce of gold @$1,250/ounce at the end of 2015 and to sell a second lot of 1.5 million ounces @$1,370/ounce at the end of 2016. As of the end of 2014, say the spot price of gold is $1,350/ounce, and the continuously compounded risk-free rate is 10% (ignore other carrying costs). Calculate the aggregate marked to market value of Zarrick’s forward contracts at the end of 2014.

IN-CLASS WORKOUT # 4 A stock is expected to pay a dividend per share of $30.00 in 1 month (t=1) and $30.00 in 4 months (t=4). An investor has just (right now, t=0) taken a LONG position in a 6-month maturity forward contract on the stock and didn’t make or receive any payment for initiating the forward position. The stock price now (t=0) is $630 and the risk-free interest rate is now 12% per annum with continuous compounding for all maturities. (a) What is the no-arbitrage forward price now (at t=0)? (b) Two months later (t=2), say the risk-free interest rate is still 12% and the stock price reaches a level of $378. Upon agreement with the counterparty to terminate the contract at that time (t=2), how much should the investor pay or receive?

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IN-CLASS WORKOUT # 5 You can borrow cash at an interest rate of 9.00% per annum or borrow gold bullion at an in-kind interest rate of 1.65% per annum. These rates are quoted on an annual compounding basis. On a continuously compounded basis, the risk-free rate is 5.00% per annum and the gold storage costs are 1.20% per annum. Currently gold is selling in the spot market at $1,340 per ounce. Assume that you borrow one ounce of gold in the spot market for a year or borrow in cash the current spot value of one ounce of gold for one year. [Ignore credit risks]. (a) Which type of borrowing is better for you on a future value basis? (b) At what in-kind interest rate for borrowing gold bullion (Annual Percentage Rate, rounded to two decimal places) you will be indifferent between the two investment choices? (c) At what interest rate for borrowing cash (Annual Percentage Rate, rounded to two decimal places) you will be indifferent between the two investment choices?

Mo Chaudhury, Derivatives

IN-CLASS WORKOUT # 6 Find out the “?” figures.

IN-CLASS WORKOUT # 7 Fill up the shaded cells and Find out the “?” figures.

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IN-CLASS WORKOUT # 8

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IN-CLASS WORKOUT # 9 Structured Note with BSM

A client of your bank wants to buy a structured with the note payoff at maturity (T) linked to the asset price (ST) at that time. The client wishes to incorporate/embed into the note the dollar payoff (not profit) of a standard short strangle on the asset with K1=$85 and K2=$115. If the dollar payoff of the standard short strangle is $X, then the note payoff at maturity will be $125 + 1.20$X. What is the RN probability, %, rounded to two decimal places,that the note payoff at maturity will be below $125? What is the RN Expected Payoff, rounded to two decimal places, of the Note? What is the value now of the Note? To sell the note at par (=Face Value), if the note payoff is set to A+1.20 $X [instead of $125+1.20$X], what should be the value of A?

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IN-CLASS WORKOUT # 10 Dynamic Replication with BSM Consider the following information on 1-year maturity options on one share of GEN generated by the Black-Scholes-Merton (BSM) Model.

Dynamic replication of a bull put spread (K1=700, K2=760) would involve what positions in the share and risk-free lending/borrowing? Long 0.0625 Shares, Borrow $76.02 Suppose you could buy or sell the given maturity Strangle (K1=640, K2=760) for $260.94 in the market. [Based on options on one share]. What would be the riskless arbitrage strategy? Long 0.3046 Shares, Lend $4.22

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IN-CLASS WORKOUT # 11 Option Strategy with BSM It is October 2012 and the market prices for January 2013 maturity ZPLN options are as follows:

You expect that ZPLN shares will fluctuate laterally (range bound) between $475 and $525, until after January 2013 option expiration. You do not have any view on the most likely share price at maturity within the specified range. However, you believe that the chances are rather low that ZPLN shares will break too far below $475 or above $525 by January 2013 option expiration. Your risk tolerance level is very high and you prefer a credit strategy. Your estimate of expected return ( μ) and volatility (σ) of ZPLN are 15% and 50% respectively, per annum. Use the actual, not the risk-neutral distribution here. Under the most suitable strategy, what is the probability, %, rounded to two decimal places, of a loss (negative profit) at maturity? 41.73% Under the most suitable strategy, would a positive profit at maturity realize if the asset price at maturity (ST) is $380? $620? No Under the most suitable strategy, what is the probability, %, rounded to two decimal places, of a positive profit of more than $60.59 at maturity? 25.15%...