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Mathematics for finance, 2023 Suppose that today's stock price is 100 yen and the stock price will be 130 yen or 80 yen one year later. Consider the option to give the right to buy the stock for 100 yen one year later. Find the option price.
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- Suppose you buy a one-year European call option on Apple with an exercise price of $100 and sell a one-year put option with the same exercise price. The current stock price is $100, and the interest rate is 10%. Draw a position diagram showing the payoffs from your investments. How much will the combined position cost you?What is the appropriate risk-free rate on May 11, 2022 for an option that expires on Oct 20, 2022 if the T-bill with closest maturity is quoted as 3.65/3.44? a. What is the un-annualized discount rate? Round your answer to two decimals. b. What is the T-bill price? Round your answer to two decimals b . What is the approximate risk-free rate? % Round your answer to two decimalsA put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 – $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 – $1.00 =…
- To a first approximation, one can think of the stock market as a perpetuity with a roughly constant dividend payment. If the Federal Reserve increases interest rates at the next FOMC meeting on March 16 2022, what will happen to the value of the stock market? Question 1 options: a. It will go up. b. It will go down. c. Interest rates have no bearing on the stock market. d. It depends on what investors expected the Federal Reserve to do.A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 - $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 - $1.00 =…A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a six-month European put option for a share of stock with an exercise price of $26. If six months later, the stock price per share is $26 or more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $26 − $22.50 = $3.50 per share, less the cost of the option. If you paid $1.00 per put option, then your profit would be $3.50 − $1.00 =…
- Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (c) What is the price of a call option on the same stock with the same exercise price and the same expiration date? Explain the reasoning behind your your calculations.Suppose today you buy a coupon bond that you plan to sell one year later. Which of the rate of return formula incorporates future changes into the bond's price?A put option in finance allows you to sell a share of stock at a given price in the future. There are different types of put options. A European put option allows you to sell a share of stock at a given price, called the exercise price, at a particular point in time after the purchase of the option. For example, suppose you purchase a she-month European put option for a share of stock with an exercise price of $25. tf six months later, the stock price per share is $26 more, the option has no value. If in six months the stock price is lower than $26 per share, then you can purchase the stock and immediately sell it at the higher exercise price of $26. If the price per share in six months is $22.50, you can purchase a share of the stock for $22.50 and then use the put option to immediately sell the share for $26. Your profit would be the difference, $25-$22.50-$3.50 per share, less the cost of the option. If you paid $1.00 per put ption, then your profit would be $3.30-11.00-$2.50 per…
- Suppose the European call and put options with strike price $20 and maturity date in 1 month cost $2.0 and $1.0, respectively. The underlying stock price is $18 and the risk-free continuously compounded interest rate is 8%. (a) Is there an arbitrage opportunity? (b)If yes, how would you implement arbitrage opportunity?Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (a) Calculate the value of the put option using the risk-neutral valuation relationship (RNVR). Explain the reasoning behind your calculations.Consider a put option on a stock that currently sells for £100, but may rise to £120 or fall to £80 after 1 year. The risk free rate of return is 10%, and the exercise price is £90. (b) Calculate the value of the put option by using first principles (No Arbitrage prin- ciples). Explain the reasoning behind your calculations.