RPT : Random Pricing Theory

This note illustrates a revolutionary pricing theory for assets particularly derivatives which depend so much on random behaviour of underlying market variables.
This is revolutionary in a sense that it has almost zero correlation with market movements. This however is a copyrighted theory and usage of this to price derivatives and structured products will be charged on a case by case basis.

Following is the theory

Consider a derivative say, a swap. We start with a guess of its price, Say X. Now we introduce random variables to converge the price to its fair value. The fairness is achieved by a total non-biasedness of the sampled data. We use a trinomial tree approach to price these securities. We also segregate the direction (up, down and no movement) from the quantification of the movement.

To achieve non-biasedness, we use parrots to sample. One parrot is used to determine the direction of movement and other to quantify the volatility. To know direction one parrot is used to toss a coin (teaching the parrot to toss a coin is achieved using another theory. Please refer appendix). Depending upon the outcome of the toss. Our sample space contains the following outcomes. { head, tail, standing coin}. We define a random variable C as follows

head = +1
tail = -1
standing coin = 0

Another parrot is used to determine the quantity of movement say Q. Now choosing the quantity can be a discrete or a continous process. For a discrete one we use a dice or a card. dice has lower number of outcomes so its volatility is lower.

For a continous one we can use a circle where the parrot runs around the circumference and depending upon the point where it stops the distance is calulated as the difference between the initial and final point. This distance is the random variable. We can have a multiplier to the distance to find the quantity of movement. The parrot either picks a card, tosses a dice or runs on a circle. This gives the quantity.

The ultimate movement is determined as follows. The final movement is

C*Q.

Hence the final price is

X + C*Q.

This experiment is repeated till both the parrots faint. Then the average of the prices is taken and this is the correct and fair price.

The above method is a generalized one. Care should be taken to choose parrots of only those region from where the security originates. Parrots can be shown a video of the market or stock exchange if you want to achieve some correlation to the market.

Addendums to follow

XantoZ