Option Pricing And Risk Analysis On Bubble Market

B-S formula is based on the hypothesis that market is complete and perfect , but the reality of financial markets and trading environment don't like that, which affected the practicality and authenticity of the pricing formula. In order to better suit the reality, assumptions must be relaxed accordingly. In an imperfect market, hedging strategies and option pricing methods should make another adjustment. Price with bubble is an adjustment to perfect market, where the stock price is not a martingale, but a local martingale. As the underlying price has bubble, the risk faced by derivatives positions increases, so there are important practical significance to study on the option pricing and the risk metrics of bubble market. This paper introduces the definition of bubble, as well as several major non-martingale bubble mathematical models; Use super-replication method, we deduced pricing formula of all kinds of options; we also discussed pricing formula's features and application. When the stock price contains bubble, Option Pricing will be different from it on the perfect market but has a special nature: P-C parity formula fails; American option has no optimal execute time; Path depended option may have infinitude Value and so on. Market bubble will permit arbitrage opportunity, so we should set some restrictions to restrain arbitrage in continuous transaction model. Generally, stock exchange restricts the assets ratio of being shorted to avoid arbitrage. The super-replication method just permits portfolio constraint, so we can take advantage of this method to price the options on bubble market. As an example, we compute upper hedging price of European Option under the CEV model. An application of Option Pricing Formula is estimating the value of mortgage risk. Finally, we analysed the credit risk when collateral price has bubble. Through analysing the credit risk value, mortgage rates, default probability, as well as the risk prior to maturity of the bubble market, we gained the relationship between the risk and these indicators, and concluded that the potential credit risk increases when bubble exists and should arouse our attention.