tailieunhanh - Lecture Financial modeling - Topic 13: Option contracts and hedging, monte carlo valuation, and black-scholes

Topic 13 - Option contracts and hedging, monte carlo valuation, and black-scholes. After completing this unit, you should be able to: Compute the payoffs and profits of plain vanilla option contracts, value options using monte carlo simulation and black-scholes models, computed hedged and unhedged cashflows using options and forwards, value arithmetic asian options, use @Risk to value options and compute position risk. | Financial Modeling Topic #13: Option Contracts and Hedging, Monte Carlo Valuation, and Black-Scholes L. Gattis 1 Learning Objectives Compute the payoffs and profits of plain vanilla option contracts Value options using Monte Carlo Simulation and Black-Scholes models Computed hedged and unhedged cashflows using options and forwards Value arithmetic Asian options Use @Risk to value options and compute position risk 2 Option Contract A call option is a contract to buy an asset in the future in which the asset, price, quantity, delivery place and location, are specified in the contract. The owner of the call has the choice to exercise the option, pay the exercise (., strike) price, and take delivery of the asset. The seller of the call is obligated to deliver the asset and receive the strike price if the buyer exercises. A put option is a contract to sell an asset in the future in which the asset, price, quantity, delivery place and location, are specified in the contract. The owner of the put has the choice to exercise the option, receive the exercise (., strike) price, and delivers the asset. The seller of the put is obligated to take delivery and pay the strike price if the buyer exercises. There is a cost to acquiring a call or put. The buyer of the call or put pays the seller a premium. 3 Option Characteristics Underlying asset: Stock, Bond, Currency, Commodity, Futures contract Option Cost (., Premium, Price) Option Type: Call or Put Exercise Type European: Exercise only at maturity American: Exercise anytime up to maturity Option Maturity Option Strike ATM: Strike = Current Spot ITM: Strike Spot for put OTM: Strike > Spot for call, Strike < Spot for put 4 Forward vs. Option Payoffs 5 Long Forward Payoff = (St-f)Q - Obligated to take delivery and pay f, can then sell in spot market Short Forward Payoff = (f-St)Q - Obligated to deliver and receive f, acquiring asset in the spot market Long (buyer) Call Payoff = Max(St-X, . | Financial Modeling Topic #13: Option Contracts and Hedging, Monte Carlo Valuation, and Black-Scholes L. Gattis 1 Learning Objectives Compute the payoffs and profits of plain vanilla option contracts Value options using Monte Carlo Simulation and Black-Scholes models Computed hedged and unhedged cashflows using options and forwards Value arithmetic Asian options Use @Risk to value options and compute position risk 2 Option Contract A call option is a contract to buy an asset in the future in which the asset, price, quantity, delivery place and location, are specified in the contract. The owner of the call has the choice to exercise the option, pay the exercise (., strike) price, and take delivery of the asset. The seller of the call is obligated to deliver the asset and receive the strike price if the buyer exercises. A put option is a contract to sell an asset in the future in which the asset, price, quantity, delivery place and location, are specified in the contract. The owner