Nature of Derivatives

A derivative is an instrument whose value depends on the values of underlying instrument.

Derivatives

Forward Contracts: Custom made contracts to buy/sell the underlying asset

in the future at a fixed price. Maturity and size of the contract can be determined individually to almost exactly hedge the desired position.

Futures Contracts: Ready-made contracts to buy/sell foreign exchange in

the future at a specific price. Contract’s liquidity is guaranteed by the exchange on

which it is traded. Too structured, margin requirements cause cash flow

uncertainty.

Options Contracts: Offer the right, but not the obligation, to buy/sell foreign

exchange in the future at a specified price. Allow hedging contingent risks.

Swap Contracts: Contracts which involve two counter parties exchange

over an agreed period, two streams of payments.

Forward Contract

Early Delivery Customer receives/requires the foreign currency earlier

than the original contract date.

Extension When he informs that he expects to receive/pay at a

later date than the contract date.

Cancellation Customer receives/requires the foreign currency earlier

than the original contract date

Cancellation Customer requests the banker to cancel the contract

because he may not receive/pay foreign currency that was originally supposed to have been received/paid.

Early Delivery

Forward Purchase Contract for the customer/Forward sale for the banker

Original: Bank buys forward from market.

Now: Buys spot and sells forward to square up the buy position entered earlier.

Swap charges: If loss is incurred, the same would be received from the customer. In case of gain the same would be paid.

Extension

Customer requests for extension

Existing contract is cancelled

Rebook the forward date

Extension

Forward Purchase Contract

Original: Bank buys forward

Now: Banker would sell spot to square the buy position.

Purchases forward for new due date.

Cancellation charges: If loss is incurred, the same would be recovered. If gain, the same would be paid to the customer.

Cancellation

The bank shall recover or pay as the case may be, the difference between the contracted rate and the rate at which the cancellation is effected.

Early Delivery -Charges

If loss is incurred, the same would be recovered from the customer.

If gain, the same would be paid to the customer.

Options-Types

Call Option

Put Option

Options -Exercise

ITM

ATM

OTM

Options- Styles

American

European

Option Premium

Intrinsic Value

Time Value

Option Strategies

Buy a call Market view Risks Reward

E.g An oil refiner is concerned that crude oil prices may rise but he does not want to lock in a firm price by purchasing a futures contract. The refiner then buys a crude oil call.

Sell a call

Market View Risks Reward

E.g A Fund manager investing in T-bonds wishes to enhance the yield on her portfolio. She has the view that market will remain stable or fall slightly over the next few months. The current T-bond price is $100 and so the manager sells a call a 100 call with a premium of $4.

If the option is exercised she has to deliver the T-bonds from her portfolio.

If the option is not exercised the premium received enhances the profits.

Buy a Put Market view Risks Reward

Sell a put Market view Risks Reward

Straddle – Simultaneous buying/selling options of different types with the same strike price.

Long Straddle: Buy a call and Buy a put with the same strike price. Market view: Significant price changes Risks: Limited to the premium Reward: Call option exercise with unlimited profit

potential, if price rises. Put option exercise with large but limited profit, if price falls.

E.g. Buy 1 March 5.00 Call 0.10 Buy 1 March 5.00 Put 0.10 Break-even point: 4.80 or 5.20

Short Straddle: Sell a call and sell a put with the same strike price. Market view: Little or no movement Risks: Call option gets exercised, with potential

unlimited loss for the writer. Reward: Limited to the premium paid.

Strangle: Simultaneous buying or selling of options of different types with different strike prices.

Long Strangle: Buy a put with a low strike price and buy a call with high

strike price. Market view: Major movement, unknown direction. Risks: Limited to the net premium paid. Reward: Huge profit potential, if movement is

substantial. Cost of strangle is cheap.

E.g Buy 1 March 3.00 Put 0.05 Buy 1 March 4.00 Call 0.10 Break-even point: 2.85 or 4.15

Short Strangle: Sell a call with a high strike price and sell a put with low

strike price. Market view: Little or no movement. Risks: Unlimited loss potential Reward: Limited to the net premium.

Spread: Simultaneous buying and selling of options of the same type with different strike prices.

Bull Call Spread: (Long Call Spread) Buy a call with low strike price and Sell a call with high strike

price. Market View/Strategy/Advantage/Disadvantage

– Market will rise to a certain level. – Take advantage of bullish opinion– Reduce cost by selling a call– Sacrifice potential unlimited profit

Risks: Limited to the net premium Reward: Limited to the difference between the two strike price

less net premium received.

E.g: Buy 1 April 4.00 Call 0.50 Sell 1 April 4.50 Call 0.30 Break-even: 4.20 Maximum Profit: 0.30 Maximum Loss: 0.20

Bear Put Spread: Buy a put with high strike price and Sell a put with low

strike price. Market View/Strategy/Advantage/Disadvantage

– Market will fall to a certain level. – Take advantage of bearish opinion– Reduce cost by selling a put– Sacrifice potential large profit

On April 28, you purchased a European call option on GBP at a strike price of $1.4000 for a premium of $0.07. The spot rate at the time was 1.4500. The expiry date is October 16.The amount of underlying is GBP 62500.

Compute the premium Check whether is ITM/ATM/OTM Check the intrinsic value/time value of the option On expiry, suppose the spot rate is GBP/USD 1.4800, what is

the net gain/loss?

Premium = $(62500x0.07) = $4375 Strike price < Current spot = ITM Intrinsic value = USD 0.05 per GBP. Time value = USD 0.02 per GBP. Should exercise the option

Gross profit = 1.4800-1.4000 = 0.08 Net Profit = 0.08 – 0.07 = 0.01 Total profit = 0.01 x 62500 = 625 per option contract.

The current CHF/USD spot is 0.6675. The following 90-day call options on CHF are available:

Your view is that CHF is going to make a strong up-move during the next 90 days. Your risk appetite is moderate. What strategy is suitable for you?

– STRIKE PREMIUM USD per CHF USD per CHF 0.6000 0.075 0.6500 0.030 0.7000 0.010 0.7500 0.002

A bullish call spread Buy a call with strike 0.6000 and sell a call with

0.7000. Net premium is USD 0.07. If the CHF moves above 0.67 you will make net gain. If CHF is 0.72, purchased call makes a profit of 0.12

and sold call makes a loss of 0.02. Net premium is 0.07

Profit = 0.12-0.02-0.07 = 0.03

A German firm buys a call option on $100,000 with a strike price of DEM 1.60/$ and a premium of DEM 0.03/$.The interest opportunity cost is 6% p.a and maturity is 180 days.

What is the B.E maturity spot rate beyond which the firm makes a net gain?

Suppose the 6-month forward rate at the time the option was bought was DEM 1.62/$. What is the range of maturity spot rate for which the option would prove to be better than the forward cover?

The premium would be DEM 30000 and interest on it for 180 days would be DEM 900. Thus per dollar cost of premium and interest would be DEM 0.0309.

Since the strike price is DEM 1.60, the breakeven rate will be DEM 1.6309 per

dollar.

For maturity spot rate up to DEM (1.6200-0.0309) = DEM 1.5891, option would

be better than forward. Beyond that forward would be better.

A French exporter to U.K has 90 day Pound receivable. He purchases a put option on GBP 250,000 at a strike price of FRF 8.0550/GBP at a premium of FRF 0.20 per Pound. The current spot rate is FRF 8.1000/GBP and the 90-day forward is 8.0750. The interest opportunity cost for the firm is 9%p.a.

Calculate the maximum FRF/GBP rate at the end of 90 days below which the firm will make a net gain from the Put.

Calculate the range of maturity spot over which the option would be better than the forward and vice-versa.

Including interest, the premium cost is FRF 0.205 per pound. Maturity spot must be below (8.0550-0.2050) = FRF 7.8500 for the put to make money on a net basis.

For maturity spot rate above (8.0750+0.2050) = 8.2800, put is better than forward; below that forward is better.

Futures

On April 29, you bought a June futures contract on GBP at price of $1.5450. The contract size is 62500 GBP, the initial margin is 5%. On April 30, May 1 and May 2 the prices closed at 1.5490,1.5460 and 1.5410. Determine the variation margins and the balance in your account at the close of April 29,30, May 1 and 2nd.

The initial margin is $0.05(62500x1.5450) = $4515.62

Cl.Price Gain(Loss) Balance

April 29 4828.13

April 30 1.5490 0.0040(62500) 5078.13 May 1 1.5460 -0.0030(62500) 4890.63 May 2 1.5410 -0.0050(62500) 4578.13

Futures Price Determination

A futures contract on CHF expires 82 days from today.

Spot CHF/USD : 0.6050 Futures price : 0.6565 82 day Euro dollar interest rate : 5.25% Euro CHF rate : 4.50%

Borrow $100 Repayment = 101.17 (1.17% for 82 days) Convert to spot CHF = 165.28 Invest CHF = 166.67 (1.01% for 82 days) Sell CHF futures = 109.42 Profit = 8.25

Assume the futures price was 0.6060 Covered interest arbitrage would have been

close to Zero.

Futures Price & Spot Price

Crude oil producers are worried about falling oil prices. They would like to hedge their risk by selling futures contract which will fix their delivery prices.

Purchasers –Crude oil refiners Assume Refiners demand fall short of supply. Speculators, if they expect a price rise will fill the gap

so that they can make profit

Difference between spot price and futures price – Basis

Current futures price > Expected spot price at maturity – Normal Backwardation

Current spot price < Current futures price Contago (Positive Basis)

Current spot price > Futures price – Backwardation

On Feb12 you see the following quotes: GBP/USD spot : 1.4650 March GBP futures : 1.4425 June : 1.4250 Sep : 1.3850 Dec : 1.3550 You agree with the direction of movement in the GBP/USD rate

implied by these prices but feel that the market is overstating the extent of likely movement. In particular you feel the market is overstating the movement between Sep & Dec. You wish to profit from your view but do not wish to take too much risk. You feel your view would materialize by early Sep. What should you do?

GBP will fall by 3 cents between Sep and Dec.

Dec contract is underpriced Sell Sep at 1.3850 and buy Dec at 1.3550

On Sep 2 the GBP/USD spot is 1.3950, Sep futures are 1.3940 and Dec futures are 1.3895. Work out gains/losses for the strategies.

Sep 2 – Square off Buy Sep at 1.3940 and Sell Dec at 1.3895 Loss on the former:

$(+1.3850-1.3940) = $0.09 per GBP

Gain on the latter: $(-1.3550+1.3895) = $0.0345 per GBP

The current CHF/USD spot is 0.6675. The following 90-day call options on CHF are available:

Strike Price Premium0.6000 0.0750.6500 0.0300.6800 0.0100.7000 0.0050.7500 0.002

Your view is that CHF is going to make a strong up-move during the next 90 days. Your risk appetite is moderate. What strategy is suitable for you?

Bullish call spread Buy a call with strike 0.6000 and sell a call with

0.7000. Net premium is USD 0.07. If the CHF moves above 0.67 you will make net gain. If CHF is 0.72, purchased call makes a profit of 0.12

and sold call makes a loss of 0.02. Net premium is 0.07

Profit = 0.12-0.02-0.07 = 0.03 Max Loss = 0.07 if CHF moves below 0.07

The current $/Yen spot rate is 123. 6 month European calls with strike $0.0087 and $0.0083 are trading at premia of 0.015cents per Yen and 0.02 cents per Yen respectively. A speculator is expecting a fairly strong appreciation of yen over the next six months. What option strategy should he adopt to profit from this forecast? What is break even rate?

A limited risk speculative strategy would be the bullish call spread i.e. buy the call with strike $0.0083 or 0.83 cents per yen and sell the call with strike $0.0087 or 0.87cent per yen.

The initial investment would be (0.02-0.015) = 0.005 cent per yen. The breakeven spot rate would be 0.83+0.005 = 0.8350 cent per yen.

Maximum profit potential would be (0.87-0.83) – (0.02-0.015) = 0.035 cent per yen.

The current USD/NLG spot rate is 0.5410.The following 2 month calls and puts are available:

A speculator expects the USD/NLG rates to hold fairly steady over the coming quarter with only small movements around the current spot rate. What strategy should he adopt to profit from this view if at the same time he wishes to limit his max loss?

Sell a butterfly spread Sell two calls with strike 0.55 and buy one call each

with strike 0.50 and 0.60. Profit over the range (0.5000+0.0080) and (0.6000-

0.0080) i.e. 0.5080 and 0.5920. Maximum profit will be (0.05-0.008) or 0.0420 and

the maximum loss would be 0.008.