HOME ASSIGNMENT

PROBLEM 1

What is a forward price of an index JKL given the following information?

Date of pricing: November 15, 2019

Time till expiration: four months / Contract expires on March 15, 2020

Current value of an index: 2 803

Continuously compounded interest rate: 4.5 %

Continuously compounded dividend yield: 2.3%

PROBLEM 2

What is the value of the forward contract (specified in problem 1) on January 15, 2020 if:

Forward price of contract with the same underlying assets that expires on March 15, 2020 is 2 790

Forward price of contract with the same underlying assets that expires on May 15, 2020 is 2 980

PROBLEM 3

In 270 days, a US-based company expects to borrow $ 15,000,000 for a period of 90 days at 90-day Libor set in 270 days. The company is concerned that rates may increase.

At time 0, this company enters a 9 12 FRA, an instrument that expires in 270 days and is based on 90-day Libor. The company will receive floating (long position).

At time 0:

90 -day Libor in USD (Lh) is 1.7%.

270 -day Libor in USD (Lh) is 2.1%.

360 -day Libor in USD (Lh) is 2.5%.

After 90 days:

90-day Libor in USD (Lh) is 1.62%.

180-day Libor in USD (Lh) is 1.9%.

270 -day Libor in USD (Lh) is 2.05%.

360 -day Libor in USD (Lh) is 2.5%.

After 270 days:

90-day Libor in USD (Lh) is 1.75%.

270 -day Libor in USD (Lh) is 2.2%.

360 -day Libor in USD (Lh) is 2.6%.

What is a price of this FRA at time 0?

What will be the payment paid or received to settle this contract? Further, please specify what party will make a payment and when?

What will be a value of an existing 912 FRA to the short and to the long parties 90 days from initiation of that contract?

PROBLEM 4

Using the BSM model, estimate value of a 3-month call option and 3-month put option on a share of ETF if:

an exercise price, X: $250

sport price, S0: 260

the annual risk-free rate is 5 %

historical standard deviation of shares returns: 12%.

Implied standard deviation: 13.5%

Please show how you calculated the following parameters: d1, d2, N(d1). N(d2), N(-d1), N(-d2)

PROBLEM 5

A Japanese importer is planning to pay 1.2 mln British pounds for goods to be received. The current exchange rate is 1 GBP = 139.577 JPY or 1 JPY = 0.00716451 GBP

Please indicate what strategy with a use of options should be followed by a Japanese importer in order to have a protection against an adverse movement in the exchange rate.

In your analysis, you need to indicate what are the base and pricing currency.

For a chosen by you strike price (you need to justify the strike selected), estimate value of an option (type of an option, call of put, should be selected by you and justified), given that:

The annualized UK risk-free rate is r= 3.5 %, and the Japanese rate is r= 4%.

The time to expiration (T) is 0.25 years,

Historical volatility of the exchange rate =10%

Implied l volatility of the exchange rate =8.5%

PROBLEM 6

Estimate value of a put and a call option on interest rate given the following information:

Notional amount 2 500 000 USD

Strike rate on 90-day Libor is 3 %

Both options mature in 6 months

At time 0:

90-day Labor: 2.7

180-day Libor: 2.9

270 day Libor: 3.05%

360-day Libor: 3.1%

In 180 days:

90-day Labor: 2.8

180-day Libor: 2.95

270 day Libor: 3.05%

360-day Libor: 3.15%

Historical : 7%

Implied volatility: 7.5%

PROBLEM 7

Consider the following three period interest rate lattice by year:

Using the binominal model value three-year European put option with the periodically computed one-year interest rate as the underlying. Assume the notional amount of an option is $100,000, the strike rate is 2.5% of par, and the risk neutral (RN) probability of an up jump is 55%.

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