I am in possession of two coins. One is fair so that it lands heads (H) and tails (T) with equal probability while the other coin is weighted so that it always lands H. Both coins are magical: if either is flipped and lands H then a $1 bill appears in your wallet, but when it lands T nothing happens. You may only flip a coin once per period. The interest rate is i per period. You are risk-neutral and thus only concern yourself with expected values (and not variance). For simplicity, in the questions below assume you will live forever.
I am in possession of two coins. One is fair so that it lands heads (H) and tails (T) with equal probability while the other coin is weighted so that it always lands H. Both coins are magical: if either is flipped and lands H then a $1 bill appears in your wallet, but when it lands T nothing happens. You may only flip a coin once per period. The interest rate is i per period. You are risk-neutral and thus only concern yourself with expected values (and not variance). For simplicity, in the questions below assume you will live forever.
- Suppose now that I also do not know which coin is fair and which is weighted. You pick one of the two coins at random.
(a) What is your
(b) What is your willingness to pay for an option* to purchase the coin, where the option works as follows: you may flip the coin once and observe the outcome. Then, if you wish, you may purchase the coin from me for the amount you determined in part 4(a).
*The owner of an option has the right, but not the obligation, to purchase an asset for a specified price at a specified future date.
(c) What is your willingness to pay for an “n-option,” which works as follows: you may flip the coin n-times and observe the outcome. Then, if you wish, you may purchase the coin from me for the amount you determined in part 4(a).
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