Spread option pricing calculator
The following exercises introduce new concepts and clarify old ones. You will be responsible for knowing the topics covered in this exercise set. In some of the questions below you will be asked to explain your answers intuitively. This means that I want an explanation that rests on the economics of the situation and that does not rest upon formal mathematical reasoning.
Try to derive a formula for put-call parity, that is, give an intuitive justification for the following formula:. In other words, justify the statement that buying a call option, shorting a put option of the same strike and maturity, with the same underlying is the same, economically, as owning the security and financing it partially with an amount equal to the strike price of the options.
Give at least four reasons why the put-call parity relation might not hold in reality Hint: You will be graded on how specific and how convincing you are. Give at least two reasons why the relationship of put-call parity will hold approximately. An at-the-money forward call option is one which has strike price equal to the forward price of the stock.
Recall the approximate formula for such an option position:. Derive an approximate formula for the value of an at-the-money forward put option like the approximate formula spread option pricing calculator an at-the-money forward call option. Spread option pricing calculator the approximate formula, answer the following questions: Can you make money doing this? Use the approximate formula as your guide.
You spread option pricing calculator now use a free web options calculator to answer some basic questions about the properties of option prices:. For each question answer the question by spread option pricing calculator the Web based calculator to see the effect of a certain option input on option values, and then try and give an intuitive reason. What happens to the value of a straddle when the strike price increases a straddle is one call option and one put option on the same underlier, same time to maturity and same strike price?
What happens to the value of a call option as time passes, in the absense of changes in other parameters? Call an out of the money put, a put option whose strike is less spread option pricing calculator the current stock price.
Can you talk like this, without reference to the spread option pricing calculator price of the underlying, or is it necessary to speak in terms of a specific stock price? The following is an open ended question, you may answerit at any level of depth you want. A client says to you:. Can you give me an idea of how accurate it is? Provide this client with an analysis of this question. You client is not that numerically sophisticated and is looking to your understanding of mathematics, and of options pricing to give him guidance.
Spread option pricing calculator may use the Numa free options pricing calculator, or you may program in the Black-Scholes formula and use that to create an analysis. Your answer will be judged on brevity don't overwhelm you client with 50 pagesaccuracy don't give your client bad advice and clarity be clear when communicating!
A floating rate bond is a bond whose coupon interest rate floats i. That is, the coupon rate is reset periodically according to a specific rule as to when at some function of the reference rate. This is the rate, to quote Fixed Income Securities, by Frank Fabozzi, at which "major international banks offer each other on Eurodollar certificates of deposit with given maturities. The maturities range from overnight to five years.
Reference to 1-Month LIBOR means the interest rate that major international banks are offering to pay other such banks on a CD that matures in one month. A cap is a restriction on the maximum coupon spread option pricing calculator for a bond.
If an investor buys a bond with a floating rate spread option pricing calculator with an interest rate cap, you might say that the investor has entered into an option like agreement with his the issuer of the bond. Clarify exactly what this option like agreement is, and who is long the option and who is short the option there are two possibilities in each case: What is the strike price?
How do you think a maturity comes into play? What is the underlying? Why would the issuer of a bond place a cap on the coupon rate? How do you think the cap affects the value of the bond? Do you think you need option pricing formulas to make this precise?
Describe a cap on a floating rate loan. Why would the seller of a loan put a cap on the rate? A floor is the same as a cap except the restriction on interest rates is that the rates cannot fall below a certain level, called the floor.
Describe a floor as an option as in question a. Which is which is arbitrary and depends only on point of view. Now consider an example: Describe an option put or call to buy USD in terms of the underlying security which spread option pricing calculator is it?
Now, show that this is equivalent to a different option put or call with a different currency as underlier and a possibly different strike price. This equivalence can be thought of as home-foriegn parity.
Give a clear statement of home foriegn parity. Volatility, spread option pricing calculator Taleb pp. This is usually measured more precisely as the standard deviation of its future returns.
This essentially posits a distribution of future returns and then volatility is thought of as the standard deviation of this distribution. Implied volatility is the volatility that if put into the Black-Scholes formula would yield the observed market price a listed option. Option market markers often quote options in terms of their implied volatility, e.
In fact, however, options will have a bid-ask spread. This implies that implied vol will have a bid-ask spread as well. Present you final answer in a small table. Use the Numa Web calculator As an option moves into the money as its intrinsic value increases, see Taleb, p. Intuitively justify your answer.
An option is very insensitive to volatility when it is deep in the money i. As such, it is very difficult to measure implied volatility. To test this, create such an option your spread option pricing calculator by describing a strike price, a value for the underlying etc.
Also, make up a price for the option justify why you choose the price you choose. Now, use the Numa calculator to compute the stocks implied volatility. Explain the answers you get.