Definition: A derivative is a financial instrument (contract) that derives its performance from the performance of an underlying asset. Transforming the preformance of the underlying asset.

Tips：

?Contracts

?Hedge risk vs. Speculate

?Derives its performance from the performance of an underlying asset.

Forward contract:

?A forward contract is a private agreement that obligates one party to buy and the other party to sell a specific quantity of an underlying asset, at a set price, at a future date

?If the future price of the underlying assets increase, the buyer has a gain, and the seller has a loss.

A Futures contract is a specialized version of a forward contract that has been standardized and that trades on a futures exchange.

?A forward contract

?Are regulated

?Guarantee provided by the exchange through the clearinghouse

?the daily settlement for gains and losses.

A Swap contract is a series of forward contracts .

?Exchange a series of cash flows

?Default risk

An option contract:

?The owner has the right, but not the obligation to conduct a transaction

?Right and obligations are not equal only in option contract, so the long position need to pay option premium.

Advantage:

?Price discovery

?Risk management: hedge and speculation

?Lowering transaction costs

?Low capital requirement

?Greater liquidity

?Ease of going short

?Enhance market efficiency

Disadvantage:

?Too risky ? High leverage

?Complex instruments

?Sometimes likened to gambling

?Key point：

?Always increase risk? -No.

Forward

?Definition: A forward contract is a bilateral contract that obligates one party to buy and the other party to sell a specific quantity of an underlying asset, at a set price, on a specific date in the future

?Long and short forward position

?Long: buy underlying

?Short: sell underlying

?No payments will be made at the inception of a forward contract. So both parties of a forward contract is exposed to potential default risk

Risk-free arbitrage and no-arbitrage rule:

?Arbitrage involves earning over the risk-free rate with no risk or earningan immediate gain with no future liabilities

?Arbitrage opportunities: arbitrage occurs when equivalent assets orcombinations of assets sell for two different prices

?Law of one price: the condition in a financial market in which twoequivalent financial instruments or combinations of financialinstruments can sell for only one price. Equivalent to the principle thatno arbitrage opportunities are possible.

?The way of arbitrage: sell high, buy low

?If a portfolio consisting of A and B has a certain payoff, the portfolio should yield the risk-free risk

?The role of arbitrage is to eliminate mispricing and lead to the market efficiency. That is why arbitrage also plays a role in pricing.

Settling a forward contract at expiration

?Physical settlement: deliver an actual asset, has storage cost, mostly used in commodity forward.

?Cash settlement: the party that has a position with negative value is obligated to pay that amount to the other party, mostly used in financial forward.

?Settling a forward contract prior to expiration

?Entering into an opposite forward contract: with an expiration date equal to the time remaining on the original contract

?Offsetting with a different party: some credit risk remains

?Offsetting with the original party: can avoid credit risk

Settlement: settle in cash, but no actual loan is made at the settlementdate

Futures

?Definition:

?A futures contract is an agreement that obligates one party to buy and the other party to sell a specific quantity of an underlying asset, at a set price, at a future date.

?Similarity with forward contract:

?Both are settled with assets delivered or in cash;

?Deliverable contracts obligate the long to buy and the short to sell a certain quantity of an asset for a certain price on a specified future date.

?Cash settlement contracts are settled by paying the contract value in cash on the expiration date.

?Are priced to have zero value at the time an investor enters into the contract.

Standardization：

?Futures contracts specify the quality and quantity of goods that can be delivered, the delivery time and the manner of delivery.

Clearinghouse

?Each exchange has a clearing house which is a third participant guaranteeing to each party that it ensures against the other party defaulting.

?A clearinghouse acts as the counterparty to each participant. The clearinghouse is the buyer to the seller and the seller to the buyer by crediting gains to the winners and charging losses to the losers.

?There is no need to worry about the counterparty default risk.

?Each participants are allowed by the clearinghouse to reverse their positions in the future.

Risk control of Futures contract

?Margin;

?Daily Price Limit;

?Marking to market.

?Daily Price Limit:

?Price limits are exchanged-imposed limits on how much the contract price can change from the previous day’s settlement price;

?Limit move: If traders wish to trade at prices outside these limit---no trades will take place.---the settlement price will be reported upper or lower price limits

?Locked limit: when the markets hits these limits (limit up or limit down) and trading stops.

?Marking to market：The margin requirement of a futures contract is low because at the end of every day there is a daily settlement process called marking to market.

Option

Definition of option: An option is a derivative contract in which one party, the buyer, pays a sum of money to the other party, the seller or writer, and receives the right to either buy or sell an underlying asset at a fixed price either on a specific expiration date or at any time prior to the expiration date.

?Call option: Long call & Short call

?Put option: Long put & Short put

?The seller or short position in an options contract is sometimes referred to as the writer of the option

?Prices

?Option premium: option premium paid by the buyer of option;

?Exercise price: Strike price (X) represents the exercise price specified in the contract.

It’s more easy to conceive of derivative that would produce identical payoffs than many investments .

?The payoffs for most derivatives come directly from the value of the underlying at the expiration of the derivative.

?The value of the derivative at expiration is certain.

?The price of the derivative is tied to the price of the underlying.

?The derivative can be used to hedge the underlying.

?Limits to Arbitrage

?Transaction costs.

?Borrow unlimited amounts of money at risk-free rate.

?Transactions require additional capital to maintain position.

?Gains from an offsetting position might not be liquid.

?One position can not be perfect hedged in practice.

Basics of Derivative Pricing and Valuation

The price is the predetermined price in the contract that the long shouldpay to the short to buy the underlying asset at the settlement date

?Valuation of a derivative contract means determining the payoff of thecontract to the long (or short) position at some time during the life of thecontract.

?The no-arbitrage principle: there should not be a riskless profit to be gainedby a combination of a forward contract position with position in other asset.

?Two assets or portfolios with identical future cash flows, regardless offuture events, should have same price

?Risk neutrality

?Risk-neutral investors are willing to buy risky investments for which theyexpect to earn only the risk-free rate. They do not expect to earn apremium for bearing risk.

?The expected payoff of the derivative can be discounted at the risk-freerate. And should yield the risk-free rate of return, if it generates certainpayoffs

T-Bill Forward

Equity Forward

Bond Forward

Valuation of Futures Contracts

?The value of a futures contract is zero at contract inception.

?Futures contracts are marked to market daily, the value just after marking to market is reset to zero.

?Between the times at which the contract is marked to market, the value can be different from zero.

V (long) = current futures price ? futures price at the last mark-to-market time.

?Another view of futures: settle previous futures, and then open another new futures with same date of maturity.

Replication: replicate the payoffs on one asset or portfolio with those of a different asset or portfolio.

?A risk-free asset (or portfolio) can be created from a position in the underlying asset that is hedged with a position in a derivative security.

?Asset + Derivative = Risk-free asset

?Or

?Asset - Risk-free asset = - Derivative

?Derivative - Risk-free asset = - Asset

Proof of Price Parity through Replication

Put – Call – Forward Parity

Option Pricing – Binomial Model

Risk management applications

Basic Concepts

?The key here is your ability to interpret option payoff diagrams andcalculate profit/loss diagrams

?Option positions

?Buyer of a call option - long position.

?Writer (seller) of a call option - short position.

?Buyer of a put option - long position.

?Writer (seller) of a put option - short position.

Buying a call

?Value at expiration of buying a call: max(0,S-X)

?Profit from buying a call: value at expiration minus option premium, max(0,S-X)-c

?Maximum profit: infinite

?Maximum loss: option premium (c)

?Breakeven underlying price at expiration: exercise price plus option premium (X+c)

?When selling a call, these results are reversed

?Value at expiration of selling a call: -max(0,S-X)

?Profit from selling a call: option premium minus value at expiration, -max(0,S-X)+c

?Maximum profit: option premium (c)

?Maximum loss: infinite

?Breakeven underlying price at expiration: exercise price plus option premium (X+c)

Buying a put

?Value at expiration of buying a put: max(0,X-S)

?Profit from buying a put: value at expiration minus option premium, max(0,X-S)-p

?Maximum profit: exercise price minus option premium (X-p)

?Maximum loss: option premium (p)

?Breakeven underlying price at expiration: exercise price minus option premium (X-p)

?When selling a put, these results are reversed

?Value at expiration of selling a put: -max(0,X-S)

?Profit from selling a put: option premium minus value at expiration, -max(0,X-S)+p

?Maximum profit: option premium (p)

?Maximum loss: exercise price minus option premium (X-p)

?Breakeven underlying price at expiration: exercise price minus option premium (X-p)

Protective Put

?A protective put is the purchase of the underlying and a put.

Protective put=S+P

?A protective put provides downside protection against a loss in value.

?If the stock price is above the strike price, you make money on the stock's appreciation but the gain is reduced by the put premium paid

?If the stock price decreases, the loss on the stock is offset by the gain on the put. The loss on the position is the put premium and any amount that the strike price is below the original stock price