You are provided with the following information on put and call options on a stock: Call price, co = $6.64 Put price, po = $2.75 Exercise price, X = $30 Days to option expiration = 219 Current stock price, So = $33.19 Put-call parity shows the equivalence of a call bond portfolio (fiduciary call) and a put underlying portfolio (protective put). Illustrate put-call parity assuming stock prices at expiration (ST) of $20 and of $40. Assume that the risk-free rate, r, is 4 percent.
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- Describe the effect of a change in each of the following factorson the value of a call option: (1) stock price, (2) exercise price,(3) option life, (4) risk-free rate, and (5) stock return standarddeviation (i.e., risk of stock).Show how you would make a portfolio delta-neutral and also self-financing by including bonds and call options to a stock that is currently traded at sh. 100, given that the delta for the call = 0.2499 and the call price = sh5.55.In the Black-Scholes option pricing model, the value of a call is inversely related to: a. the risk-free interest stock b. the volatility of the stock c. its time to expiration date d. its stock price e. its strike price
- V3. By looking at the sensivities of your portfolio to δs = -$2 and δσ = -1%, you decide to hedge delta, gamma and Vega risk of your portfolio with the underlying stock and two different options on the same asset with below data. Calculate the units of stock you need to trade to hedge away all delta, gamma and Vega risks of your portfolio.(Note that here you have to calculate the units of stock, Option A and Option B, but you will only submit the units of stock.)Discuss the risks and payoffs of the following positions, accompanied by payoff graphs. Buy a stock. Buy a call. Buy stock and sell a call option on the stock (covered call).Suppose that call options on a stock with strike prices $100 and $106 cost $8 and $5, respectively. How can the options be (the profits from option positions and the total profit).
- Consider a portfolio that consists of the following four derivatives: 1) a put option written(sold) with strike price K − 5, 2) a call option purchased with strike price K − 5, 3) a call option written(sold) with strike price K + 5, and 4) a put option purchased at strike price K + 5. All options are European.The risk-free rate is rf , the time to expiration is T, the initial stock price is S0, and the stock price atmaturity is ST . What are the payoffs at expiration of this portfolio? What must the price of this portfoliobe?Define each of the following terms:a. Derivative; natural hedgeb. Option; call option; put optionc. Long-term Equity Anticipation Security (LEAPS)d. Exercise value; strike (exercise) pricee. Binomial Option Pricing Model; Black–Scholes Option Pricing Model; riskless hedgef. Futures contract; forward contractg. Commodity futures; financial futuresh. Swap; structured notei. Inverse floaterj. Risk managementk. Speculationl. Hedging; long hedges; short hedges; perfect hedgeBy looking at the sensivities of your portfolio to ds = -$2 and So = -1%, you decide to hedge delta, gamma and Vega risk of your portfolio with the underlying stock and two different options on the same asset with below data. Calculate the units of stock you need to trade to hedge away all delta, gamma and Vega risks of your portfolio.(Note that here you have to calculate the units of stock, Option A and Option B, but you will only submit the units of stock.) Variable Option A Option B Delta (A) -0.5 0.2 Gamma (T) 0.2 0.1 Vega (v) 8
- Describe the effect of a change in each of the following factors on the value of a calloption:1. Stock price2. Exercise price3. Option life4. Risk-free rateA portfolio of derivatives on a stock has a delta of 2400 and a gamma of –10. An option on the stock with a delta of 0.5 and a gamma of 0.04 can be traded. What position in the option is necessary to make the portfolio gamma neutral? Long/Short and how many options and why?a) Carefully draw the payoff diagram of a portfolio consisting of a long position in two call options with exercise price ?, a short position in five call options with exercise price 2? and a long position in four call options with exercise price 3?. All options have the same maturity date and the same underlying stock. What reasons could a speculator have for holding such a portfolio (explain in detail)? b) Draw the profit diagram of the portfolio above (and clearly state any assumptions you make). Recall that the profit is equal to the difference between the payoff of the portfolio at expiry (maturity) date and the cost of the portfolio. Is the cost of the portfolio positive?