Suppose a one-year European put option on a stock has an exercise price of $30 and oneyear European call option on the same stock has the same exercise price of $30. The call is  worth 3$ and the put is worth 2$. If the one-year interest rate is 1.5%, what is the price of the  underlying stock, assuming no arbitrage opportunity?

Consider an American Put option with time to expiry of 5 months and a strike price of 82. The current price of the underlying stock is 80. Divide the time to expiry into five 1-month intervals. In each interval, the stock price can either rise by 6, or fall by 6, with unknown probability. The risk-free rate is 4.2% per annum, continuously compounded.  What is the value of the option. Please provide necessary calculations.

Consider two European call options on the same underlying stock, with the same strike price, but different maturities. The first one has 1 year maturity and o = 15%, if the second one has 4 years maturity what is its o?

Use Two-State Binomial Option (European) Pricing Model. Suppose you bought a stock today for $38.00. The stock price can either go up by a factor of 1.30 or down by a factor of 0.70 with equal probability in 0.50 years (or 180 days). Suppose the annual risk-free rate is 3.50% and the option exercise price is 35.00. How much should be the Call Option Value that expires in 0.50 years (or 180 days)?Enter your answer in the following format: 1.23Hint: The answer is between 6.74 and 9.38

Suppose a stock, not paying any dividend, is currently trading at $50. The annual volatility of its price is 31.55%. This implies that in a one-period binomial tree model the stock price will either be $62.5 or $40 in six months. The annual interest rate is 5%. Consider a European call option with a strike price of $50 and maturity in six months. In the one-period binomial tree model, what's the fair value of the call?

A stock price is currently $52. At the end of 9 months, it will be either $60 or $44. The risk-free interest rate is 6%. Use the no-arbitrage binomial method to calculate the value of a 9-month European call option on the stock with strike price $52. Calculate the same option value using the risk-neutral method

Suppose that a stock price is currently 61 dollars, and it is known that at the end of each of the next two six-month periods, the price will be either 18 percent higher or 18 percent lower than at the beginning of the period. Find the value of a European put option on the stock that expires a year from now, and has a strike price of 64 dollars. Assume that no arbitrage opportunities exist, and a risk-free interest rate of 10 percent.

2. The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend of $0.50 is expected in two months and again in five months. The term structure is flat, with all risk-free interest rates being 10%. Calculate the price of a European put option that expires in six months and has a strike price of $30. PY of Dividends Dividend 1* e^(-12) + Dividend 2 * e^(-12)

Consider a European call option on a stock with current price $100 and volatility 25%. The stock pays a $1 dividend in 1 month. Assume that the strike price is $100 and the time to expiration is 3 months. The risk free rate is 5%. Calculate the price of the the call option.

A stock is selling today for $110. The stock has an annual volatility of 64 percent and the annual risk-free rate is 7 percent. Calculate the fair price for a 1 year European call option with an exercise price of $95. Calculate how much the current stock price would need to change for the purchaser of the call option to break even in one year. Calculate the fair price for a 1 year European put option with an exercise price of $95. Calculate how much the current stock price would need to change for the purchaser of the put option to break even in one year. Calculate the level of volatility that would make a $95 call option sell for $30. (Use Goal Seek or Solver). Calculate the level of volatility that would make a $95 put option sell for $8. (Use Goal Seek or Solver). Please show work in excel and functions/equations used.