tailieunhanh - an introduction to credit risk modeling phần 9

Lưu ý rằng như T → ∞ các giá trị của μ và η 2 hội tụ các giá trị cố định, và sự phân bố của XT hội tụ đến một trạng thái ổn định phân phối văn phòng phẩm. Với khuôn khổ này, chúng ta có thể tìm thấy giá của một tổ chức xã hội dân gọi châu Âu. | Note that as T TO the values of M and n2 converge to fixed values and the distribution of xT converges to a steady-state stationary distribution. With this framework we can find the price of a European call CSO. Let C x r T denote the value of the option. The payoff function for this option is simply H x max ex K 0 . The closed-form solution for the call CSO is given by C x r T p r T p n2 2N di KN 2 . Here N is the cumulative standard normal distribution p r T is a riskless discount bond and di iog K M n2 d di n. n The value of a European put CSO is P x r T C x r T p r T k eMn2 2 . The option formula has some similarities with the Black-Scholes option pricing formula. However the value of a call option can be less than its intrinsic value even when the call is only slightly in the money. This surprising result is due to the mean reversion of the credit spreads. When the spread is above the long-run mean it is expected to decline over time. This can not happen in the B-S model because the underlying asset must appreciate like the riskless rate in the risk-neutral framework. The delta for a call is always positive as in the B-S framework but the delta of a CSO call decreases to zero as the time until the expiration increases. A change in the current credit spread is heavily outweighed by the effects of mean reversion if the expiration date of the call is far in the future. A credit spread collar combines a credit spread put and a credit spread call. An investor that wishes to insure against rising credit spreads by buying a credit spread call can reduce the cost by selling a credit spread put. In a credit spread forward CSF counterparty A pays at time T a pre-agreed fixed payment and receives the credit spread of the reference asset at time T. Conversely counterparty B receives the fee and pays the credit spread. The fixed payment is chosen at time t T to set the initial value of the credit spread forward to zero. The credit spread forward can also be structured .

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