#16815 - Derivatives - Banking Law Notes

Types of derivative contracts

• Definition of derivatives: A financial asset whose value is driven by the value of some other (financial) asset(s).

• Types of derivatives:

  • Forwards;

  • Futures;

  • Swaps; and

  • Options.

Forwards and Futures:

• Forward contract = Unconditional promise to buy or sell some underlying asset at a specified price (the “forward price”) on a specified date (the “settlement” or the “maturity date”).

  • This can cover financial assets and tangible assets.

  • Usually used in foreign exchange markets, where the underlying asset will be in a different currency.

• Futures contract = Similar to a forward, except the underlying asset is not actually transferred but (cash-)settled by offset and parties’ positions are marked to market on a daily basis.

  • The result form the offset = Either the buyer or the seller has to pay (depending on who wins the “bet”).

  • Mutual compensation for marginal changes (i.e. margin calls).

  • Exchange-traded.

Swaps:

• A swap is an unconditional promise between two counterparties to exchange cash flows and is calculated on a different basis form the other.

  • Interest rate swap: Based on nominal amount, fixed interest payments are exchanged for floating interest payments.

  • Currency swap: Payments in one currency are exchanged for payments in a different currency.

  • Equity swap (Contract for difference) Cashflows based on share price movements (up or down) are exchanged for a fixed “premium”.

  • Credit default swap: In exchange for a fee, one counterparty compensates the other for any losses on credit contracts with a third party.

Options:

• A right (but not an obligation) to purchase or sell an underlying financial asset at a specified price, on or by a specified date.

  • Call option = Right to buy.

  • Put option = Right to sell.

  • American Call or Put = May be exercised up to and on the expiration date.

  • European Call or Put = May be exercised only on the expiration date.

  • Warrant = Usually a call sold by the iss50uer itself, and, upon exercising it, the company will issue a new share.

• Most calls and puts are traded amongst parties who do not actually own any of the underlying assets.

• Specifications:

  • Underlying security (price at time t = s_t)

  • Strike price (K) = The price that must be paid by the option holder for exercising the option

  • Expiration date (T)

  • At the money option, strike price (K) = market price of the security at time t

  • “In the money” call = K < s_t; “out of the money” call = K > s_t

  • “In the money” put = K > s_t; “out of the money” put = K < s_t

  • Intrinsic value = s_t - K

  • Value (i.e. price) of the call or put option at time t = c_t or p_t respectively

    • Note that the value of the option is linked to the value of the underlying security, but they are not the same.

Put-call parity and option pricing

• 1-year European call with K = 50 and c₀ = 10

• 1-year European put with K = 50 and c₀ = 10

• How are these values calculated?

  • Costs incurred in buying and exercising a call option = Value of the call option + Strike price; Benefits accrued in exercising a call option = Value of the underlying security; Buying a call therefore = S_T - c₀ - K.

  • Note that we would not exercise the call option for S_T = 0 or 25, because we would actually be making a loss, and, at S_T = 50, it makes no difference whether we exercise the call option or not.

• The graphs of buying a call and buying a put are actually mirror images of each other.

• Put-call parity: c_T - p_T = S_T - K

  • Upon expiration, holding a call (being long in a call) and having sold a put (being short in a put) will yield the same pay off as holding the security (being long in the security) and having to pay K.

  • c_t - p_t = S_t - K/((1 + r_f)^(T - t))

    • This is because we must discount the value of the strike price.

• Some applications:

  • c_t S_t - K/((1 + r_f)^(T - t))

  • The fair market value of the call must always be as large as the difference between the underlying asset’s current value and the present value of the strike price.

  • Do not exercise an American call prior to expiration unless the underlying security will pay a dividend.

• Arbitrage (How to make money in a risk-free manner):

  • Assume that:

    • A share is trading for 50;

    • A 1-year call option with strike price of 50 is currently selling for 5;

    • A 1-year put option with strike price of 50 is currently selling for 2; and

    • The risk-free rate is 5%.

  • How can you make money without any risk of loss?

  • c₀ - p₀ = 5 - 2 = 3

  • c₀ - p₀ = 50 - 50/(1 + 0/0.05) = 2.38

    • There is a price mismatch here.

  • Sell a call for 5 and buy a put for 2, making a profit of 3.

  • Buy the security for 50 and borrow the present value of 50 (which is 47.62) at the risk-free rate of 5%, incurring a loss of 2.38.

  • Net profit of 0.62 as a pure, risk-free arbitrage profit.

  • All future risks are completely hedged and cancel each other out.

    • If the value of the security rises, the counterparty will exercise his call option and pay us the strike price of 50 for the security, which we use to repay the loan.

    • If the value of the security drops, we exercise our put option and get the strike price of 50, which we use to repay the loan.

  • Repeat indefinitely and make tons of money.

• Option pricing:

  • Put-call parity provides the difference between call and put.

  • It is under-determinative because it does not give us the value of call or put separately.

  • Solution = The Black-Scholes Option Pricing Formula, which assumes:

    • No dividends will be paid before on the underlying security before the expiration date;

    • Option and security can be traded constantly traded at zero costs (i.e. perfect securities market);

    • There are no restrictions against short selling any asset;

    • The risk-free rate is constant over time; and

    • The gross returns of the security are “log-normally” distributed with a volatility parameter that is constant over time.

  • Significance:

    • One of the most important advances of modern finance.

    • In combination with advances in computer technology, allowed for the financial revolution and the derivatives explosion.

    • Fischer Black a Myron Scholes were awarded the Nobel Prize in economics.

    • It is widely used in the finance industry and is fairly accurate.

    • The math is similar to that of the fundamental heat transfer equation in Newtonian physics.

Using derivatives: Hedging and Speculation

• Interest rate hedge

  • Bank receives interest from its borrowers at a fixed interest rate.

  • But bank pays interest to lenders at a floating interest rate.

  • It hedges against the risk of an increase in interest rates through an interest rate swap with a counterparty.

• Currency hedge:

  • An importer imports goods in USD by sells them in GBP.

  • He hedges against the risk of rise in the value of USD relative to GBP through a FX forward contract, which allows him to buy USD using GBP at an agreed rate.

    • This passes the risk on to the FX dealer.

• Credit default swap (“CDS”):

  • Lender lends money to a borrower.

  • He hedges against the risk of the borrower’s insolvency through a CDS, which, for a fixed fee, compels the CDS counterparty to indemnify the lender for any credit loss that he might suffer from the borrower’s insolvency.

• Speculation:

  • By reference to a reference entity or reference portfolio.

  • Synthetic CDS:

    • There is no actual exposure;

    • It is a pure bet.

Policy considerations

• Effective risk reduction through hedging:

  • Lower cost of capital;

  • Enhanced liquidity;

  • Freeing up capital;

  • Tailor-made risk tranches are attractive for investors; annd

  • Greater diversification.

• Signalling effect:

  • Effective transmission of market information through CDS spreads;

    • CDS spread = The difference between buying and selling credit insurance for particular entities.

    • It tells you what market participants think of a particular entity.

  • More efficient capital markets; and

  • More efficient investment decisions.

• Dangers:

  • Opacity;

  • Increased interconnectedness;

    • New and opaque transmission...