Fin 4710 16 and 17

Positive Gamma

means Delta will increase as theunderlying stock prices move up•This forces market makers (who are shorting the option) to buy even more shares tomaintain Delta-neutralit

Convertible bonds (or preferred stock)

may be converted into a specified number of common shares at the option of the bondholder

•The conversion price is the effective price paid for the stock

•The conversion ratio is the number of shares received when the bond isconverted

•Convertible bonds will be worth at least the straight bond value or the conversion value, whichever is greater

•Convertible bond value = Straight bondvalue + value of warrants (call options)

The floor price of a convertible bond is driven by:

our bond to stocks. Thus, the value of yourbond equals to straight bond value.•When stock price is high, you will choose toconvert your bond to stocks. Thus, payoff will bedriven by stock prices when prices are high

Before expiration, the option to convert hasoption value.

Adding the floor price and option value gives usthe convertible bond value

Conversion price

is the exercise price (strikeprice) of the option

Forward Contract

is an agreement today to buy or sell an asset on a fixed future date for a fixed price

The fixed future date is called the maturity date.

•The fixed price is called delivery price. The delivery price is to be paid atmaturity

(OTC) forward contract

a private agreement between two parties to buy or sell an asset at a set price on a future date

The delivery price is chosen so thatthe initial value of the contract is zero.

•No money changes hands when the contract is initiate

Futures

A futures contract is an agreement to buy or sell an asset for acertain priceat acertain time.

•Similar to a forward contract•The delivery price is chosen such that the value of the contract is zero•No money changes hands at initiation

•Special features of a futures contract•Standardizedcontracts create liquidity•Exchangemitigates credit risk•Settleddaily by marking to market

long position

The party who agreed to buy in a futures contract is said to have a long position

Profit to long = spot price at maturity (PT)-original futures price

short positon

The party who agreed to sell is said to have ashort position

You bet that the prices will decline

Profit to short = original futures price-spot price at maturity

Open Interest

the number of contracts outstanding

Maintenance Margin

an established valuebelow which the trader receives amargin call

How to close a futures

Enter into an offsetting trade•Long position, then short to close•Short position, then long to close•Most futures contracts are closed out before maturity. Only 1-3% of contractsresult in actual delivery of the underlying commodity.

types of derivatives

forwards, options, futures, swaps

Forwards

• Description: Customized contracts between two parties to buy or sell an asset at a specified price on a future date.

• Example: A farmer and a buyer agree to a set price for crops to be delivered in six months, protecting both from price fluctuations.

Futures

• Description: Standardized contracts traded on exchanges, obligating parties to buy or sell an asset at a set price on a specific future date.

• Example: Oil futures, where traders agree to buy or sell oil at a specified price three months in the future.

Options

• Description: Contracts giving the holder the right, but not the obligation, to buy (call option) or sell (put option) an asset at a specified strike price before or on the expiration date.

• Example: A call option on stock XYZ allows a buyer to purchase the stock at $50 per share if they choose before expiration.

Swaps

• Description: Contracts where two parties exchange cash flows or liabilities, often to manage interest rate or currency risk.

• Types:

  • Interest Rate Swaps: Exchange of fixed interest payments for floating rates.

  • Currency Swaps: Exchange of principal and interest payments in different currencies.

• Example: Two companies in different countries swap currencies to manage exchange rate risks on their respective loans.

short squeeze

A short squeeze occurs when the price of a stock or other asset that has been heavily shorted starts to rise sharply, forcing short sellers to buy back their positions to cover their losses, which in turn drives the price even higher.

Here’s how it works:

1. Short Selling: Investors "short" a stock by borrowing shares and selling them at the current market price, hoping to buy them back later at a lower price. They make a profit if the stock price falls.

2. Short Squeeze Trigger: If the stock price starts to rise instead of fall (often due to unexpected positive news or heavy buying pressure), short sellers begin to incur losses.

3. Buying to Cover: To limit their losses, short sellers buy back the stock (known as "covering") at the higher price, which adds more buying pressure.

4. Exacerbated Price Rise: As more short sellers buy back shares, the stock price continues to climb, leading to more short sellers being forced to cover, creating a vicious cycle of rising prices.

A short squeeze can lead to dramatic price increases in a very short period, as seen with stocks like GameStop in early 2021.