Reference no: EM134816 , Length: 60

Dissertation writing help - Simulating the dynamics of the risk neutral distribution

Custom Dissertation Writing Service on valuation of complex options on financial assets.

Knowledge about the dynamics of the risk neutral distribution is necessary for the valuation of complex options on financial assets. We present and discover a formalism (the twin formalism) that allows simulating how the risk neutral probability density function evolves with time. The main idea of the twin formalism is to describe the risk neutral distribution as a mixture of possible future distributions, and to simulate its time development in a simplified ("twin") model space. This approach is model independent in the sense that we may apply it to a large variety of distributions (or processes): The formalism will automatically take care of the necessary no-arbitrage conditions between the future and today's risk neutral distribution. As an illustration, we apply the twin formalism to several models and to the valuation of different options, in particular in connection with the problem of so-called smiles in implied volatility. The modeling framework is formulated in terms of probability distributions, rather than processes. This means that one does not have to specify the dynamics (i.e. stochastic differential equations) of the underlying processes. It suffices to determine the distributions only at those points of time that are relevant for the option one wants to price.