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Pricing Analytics

Pricing analytics refers to the modeling involved in asset valuation. There are various tools for the quantitative approach and these methods fall into generally following three categories, purely analytical, numerical or simulation based approaches. Though there is some overlap but the methodologies are very distinct, In the case of analytical approach there are identified close form solutions for a specific observed behavior. Note here asset is defined in a general sense of an underlying that needs to be valued and can be considered same as a liability from valuation model perspective. Also note that an analytical formulation can be as easily adapted for an underlying where we can proxy indirectly another structure that is very similar to the underlying. In other words we can find a quantitative structure that is mimicking the underlying through not the same can adapt the modeling scheme of the proxy. Thee are several examples of that in risk adaptations, including the most famous and commonly used being the HEAT wave equation proxies for Derivative valuations via Black Scholes or Forward Kolmogorov Equations are used to analytically define probability spaces which in turn can define the boundary conditions for closed form derivative valuations. We also have Maxwell-Boltzmann distribution that is applicable to finance and trading. The relevant logic is that just as particles have different energy levels in a system, financial assets have different levels of risk and return. The distribution can represent the probability of assets achieving certain returns or experiencing specific levels of volatility. By understanding this distribution, investors can make informed decisions about asset allocation, diversifying their portfolio to achieve a desired risk-return profile. In trading, understanding the distribution can help in predicting price movements and volatility, allowing traders to position themselves advantageously. The MB framework provides a mechanism for understanding the behavior of a large number of entities as in this case assets instead of particles and their distribution across various states where each state represents return levels.
Similarly Fermi-Dirac model which is applicable in quantum mechanics, primarily deals with the distribution of particles across energy states. When applied to finance, trading, and investing, one could draw parallels between the behavior of particles and the behavior of assets, stocks, or commodities in a market. There are too many examples of the analytical model application that are direct or proxied to provide an exhaustive list. Secondly we have numerical pricing frameworks among which the most common being the decision tree based method or finite difference approach. This method could be commonly modeled with binomial or trinomial trees and the most famous in case of derivative pricing is the Cox, Ross and Rubinstein Binomial tree based option pricing. Lastly in case of too complex a pricing or valuation we use the simulation based approach and that is discussed further in this site. The most important of this simulation method is Monte Carlo simulation and it is executed in multiple variation for a structured MC.

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