Find the value of the following portfolios of options at

Find the value of the following portfolios of options at expiry, as a function of the share price: (a) Long one share, long one put with exercise price E, (b) Long one call and one put, both with exercise price E, (c) Long one call, exercise price E1, short one call, exercise price E2, where […]

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Formulate the following barrier option pricing problems as partial differential

Formulate the following barrier option pricing problems as partial differential equations with suitable boundary and final conditions: (a) The option has barriers at levels Su and Sd, above and below the initial asset price, respectively. If the asset touches both barriers before expiry, then the option has payoff max(S − E, 0). Otherwise the option […]

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Set up the following problems mathematically (i.e. what equations do

Set up the following problems mathematically (i.e. what equations do they satisfy and with what boundary and final conditions?) The assets are correlated. (a) An option that pays the positive difference between two share prices S1 and S2 and which expires at time T. (b) An option that has a call payoff with underlying S1 […]

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The solution to the initial value problem for the diffusion

The solution to the initial value problem for the diffusion equation is unique (given certain constraints on the behavior, it must be sufficiently smooth and decay sufficiently fast at infinity). This can be shown as follows: Suppose that there are two solutions u1(x, τ) and u2(x, τ ) to the problem withu(x, 0) = u0(x).Set […]

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We have seen how to apply the CreditMetrics methodology to

We have seen how to apply the CreditMetrics methodology to a single risky bond, to apply the ideas to a portfolio of risky bonds is significantly harder since it requires the knowledge of any relationship between the different bonds. This is most easily measured by some sort of correlation. Suppose that we have a portfolio […]

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