Consider a market consisting of a money market account with interest rate 10% and a stuck. The stock price is initially $10. At every time step we flip a coin which lands heads with probability 0.3 and tails with probability 0.7, and is independent of all previous coin flips. When the coin lands heads, the stock price increases by 20%. When the coin lands tails, the stock price decreases by 20%. Consider a security that pays $1000 at time N = 10 if the first 7 coin tosses are heads and the last three are tails. For any other sequence of coin tosses, the security pays nothing (a) Find the arbitrage free price of this security at time 0. (b) Find the arbitrage free price of this sccurity after the first coin toss. Your answer to both parts may depend on the outcome of the coin tosses. You should express all quantities arising in your answer as decimal numbers, correct to two decimal places. That is, don't write 2(1.23 -10 + 3) if the first coin is heads in your answer. Instead cvaluate this, and get a decimal number correct to two decimal places. Consider a market consisting of a money market account with interest rate 10% and a stuck. The stock price is initially $10. At every time step we flip a coin which lands heads with probability 0.3 and tails with probability 0.7, and is independent of all previous coin flips. When the coin lands heads, the stock price increases by 20%. When the coin lands tails, the stock price decreases by 20%. Consider a security that pays $1000 at time N = 10 if the first 7 coin tosses are heads and the last three are tails. For any other sequence of coin tosses, the security pays nothing (a) Find the arbitrage free price of this security at time 0. (b) Find the arbitrage free price of this sccurity after the first coin toss. Your answer to both parts may depend on the outcome of the coin tosses. You should express all quantities arising in your answer as decimal numbers, correct to two decimal places. That is, don't write 2(1.23 -10 + 3) if the first coin is heads in your answer. Instead cvaluate this, and get a decimal number correct to two decimal places