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Specifically, for implementation of their approach, the risk-adjusted rates of price appreciation for both the asset and the option are required Precise estimation was the problem, which was made more difficult as the option s return depends on the asset s return, and the passage of time The breakthrough came in 1973 with Black, Scholes, and Merton40 They showed that as long as a risk-free hedge may be formed between the option and its underlying asset, the value of an option relative to the asset will be the same for all investors, regardless of their risk preferences The argument of the risk-free hedge is convincing, because in equilibrium, no arbitrage opportunities can exist, and any arbitrage opportunity is obvious for all market participants and will be eliminated.

Solved Problem 10.1 The inventory information of a product is given below: Jan. 1 Feb. 16 Mar. 4 Oct. 15 Inventory Purchase Purchase Purchase 12 units 8 units 15 units 10 units $15 16 18 20

Or Pao-Chi could try another approach, claiming that someone stole his private key Maybe it was protected on his hard drive using PBE, and someone cracked his password Maybe it was stored on a smart card or other token, and someone broke that device or was able to log on as PaoChi (possibly by breaking a password) If that really is the case, Pao-Chi.

did a poor job of protecting his private key, and he will still be in trouble. We return to this subject later in this chapter in the section Protecting Private Keys.

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When Daniel checks to make sure that the data has come from Pao-Chi and not someone posing as him, it s called authentication. He authenticates Pao-Chi s identity. When Daniel examines the message to make sure it has not been altered in transit, that s called data integrity checking. And when Pao-Chi can t go back on his signature, that s called nonrepudiation. In addition to privacy, these are the main areas in which cryptography benefits those who use it. Symmetric-key encryption provides privacy in that the sensitive data looks like gibberish to unauthorized eyes. Public-key technology solves the key distribution problem. A message digest either a keyed digest such as HMAC or a digital signature ensures data integrity in that what the sender sends is what the receiver receives. A digital signature also offers authentication in that the other entity in the data exchange is shown to be the entity it claims to be and the data is verified to have come from that entity. A digital signature also provides nonrepudiation in that a signer cannot later disavow any knowledge of the message.

You can use the RSA algorithm to sign, but Diffie-Hellman can be used only to perform key exchange and not digital signatures. As discussed in 4, Diffie and Hellman proposed the idea of the ultimate public key algorithm. It would be one that could be used to encrypt data. The digital signature is the reason that such an algorithm would be the ultimate algorithm. In an interview, Whitfield Diffie explained that when he heard about the NSA s secure phone system, he was less concerned with the key exchange problem than with authentication that is, verifying that you are talking to the person you think you are talking to.

After taking a physical count, we nd that we have 14 units on hand. De termine the ending inventory cost by the (a) FIFO method, (b) LIFO method and (c) weighted average. Solution: (a) FIFO method Most recent purchase (10/15) Next most recent purchase (3/4) Ending Inventory (b) LIFO method Beginning Inventory Next Purchase Ending Inventory (c) Weighted Average $778 / 45 units = $17.29 per unit 14 units on hand times $17.29 per unit = $242.06 ending inventory Solved Problem 10.2 Determine the gross pro t under the (a) LIFO and (b) FIFO assumptions, given the following information: Sales Goods available for sale Ending Inventory (under LIFO) Ending Inventory (under FIFO) $40,000 12,000 6,500 3,500 12 units @ $15 = $180 2 units @ 16 = 32 14 $212 10 units @ $20 = $200 4 units @ $18 = 72 14 $272

If the observed price of the call is above (or below) its theoretical price, risk-free arbitrage profits are possible by selling the call and buying (or selling) a portfolio consisting of a long position in a half unit of the asset, and a short position in the other half in risk-free bonds In equilibrium, no arbitrage opportunities can exist, and any arbitrage opportunity can exist..

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