A stock trading at $47 has a volatility of 30 percent. The continuously compounded risk-free rate is 6 percent. A dividend of $1.4 is expected in 4 months, and no other dividends are expected during the next 12 months. Price a European call written on this stock with an exercise price of $50 and a time to maturity of one year.

Consider a stock in two periods (two years). The stock price goes up by 30% or down by 10%in each period. Current stock price is $100. There is a European put option on the stock withexercise price $110 and time to maturity of two years. The interest rate in each period is 6%. Inthe template, Date 0 denotes today, Date 1 denotes the end of year 1 and Date 2 denotes the endof year 2. Use the two-period binomial tree model and discrete discounting to find the put optionprice on Date 0.

A non-dividend-paying stock is currently selling for $50, and the risk-free rate of interest is 8% per annum with continuous compounding for all maturities. An investor has just taken a short position in a six-month forward contract on the stock. a. What is the forward price？ (sample answer: $25.45) b. What is the initial value of the forward contract? (sample answer: $25.45) c. Three months later, the price of the stock is $48 and the risk-free rate is still 8% per annum. What is the forward price now? (sample answer: $25.45) What is the value of the short position in the forward contract? (sample answer: $25.45 or -$25.45

The market price of JS stock is currently $30. It is known that at the end of three months it will be either $33 or $27. The risk-free interest rate is 8% per annum with continuous compounding. (a) Use a one-step binomial tree to calculate the value of a three-month European put option on the JS stock with a strike price of $31? Use no-arbitrage arguments (you need to show how to set up the riskless portfolio). (b) Use the same one-step binomial tree and your results from (a) to determine the price of a three-month American put option on the JS stock with a strike price of $31

A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is 2.5%. Calculate values for u, d, and p when a six-month time step is used. What is the value a 12-month American put option with a strike price of 1,480 given by a two-step binomial tree.

A stock price is currently $40. It is known that at the end of three months it will be either $44 or $36. The risk - free rate of interest with continuous compounding is 8% per annum. Calculate the value of a three-month European call option on the stock with an exercise price of $39. Verify that no - arbitrage arguments and risk - neutral valuation arguments give the same answers.

A stock is currently trading at $54 and we assume a three-period binomial tree model where each period the stock can either increase by 20%, or fall by 18%. Each step in the tree is 3 months. The interest rate is 1.1% per year (continuous compounding). In this model, what is the risk-neutral probability that the stock price will go up twice and drop once over the three periods? [Provide your answer as a percentage rounded to two decimals, i.e. 40.25 for 0.4025=40.25%]