Boyd model

The Boyd model is a comprehensive multi factor, reverse engineered, closed end solution to fair value any illiquid security where no transparent market data exists. It is flexible and adaptable enough to value the vast majority of hard-to-price instruments but its most notable success has been in the calculating the fair value of private equity positions. The Boyd model is mean & client-price reverting model having its roots in GARCH process. These reverting factors have incorporated a factor that ensures against any wild valuation movements that would be surprising to the market or surprising to the client, whilst also maintaining a conservative valuation approach.

This flexibility and adaptability characteristic hasn’t been seen in a model since the historic and ground breaking issue of the Black–Scholes formula and the subsequent adaptation of the Black–Scholes formula for all financial option types. The Black–Scholes formula challenged modern thinking on optionality and opened up the derivative market to a massive explosion in security trading. The Boyd model is also challenging modern thinking on private equity valuation and is expected to add more visibility to the market and thus increase the investment in such positions. This was a huge influence in arriving at this solution due to the stochastic nature of the underlying data (the underlying stochastic process).

Creator

The model was written by Rog Boyd.

Evolution

To overcome the problems with pricing illiquid and private securities in the financial fund services sector, the Boyd model was developed to bring some standards to the valuation process.

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RB = arctan⁻¹ * Sinh(x^−2ey +z * f(y)^-z+q^x + r + z) * Cos(π/m). Gi * (1 / x^2y2) + x

where

x = the Dalweska–Boyd constant, in most circumstances also known as the "Clients Estimated Price"

z = the risk-free interest rate

q = Gauss's constant

r = Correlation of q and m, r ~ N(q,G)

G = 6.67300 * 10⁻¹¹m³kg⁻¹s⁻² = Gravitational Constant

m = $\lim _{x\to \infty }$ ${\frac {2\pi (x)}{\frac {x}{\epsilon ^{ln(lnx)}}}}$ where :$\pi (x)\sim {\frac {x}{\ln x}}.$

y = :$\zeta (s)=1+{\frac {1}{2^{s}}}+{\frac {1}{3^{s}}}+{\frac {1}{4^{s}}}+...........$ where s = q

Parametric data

The basic parametric data needed to calculate the formula are easily obtained and therein lies the beauty of the model. This fundamental principle of the Boyd model is what lends itself so beautifully to the valuation of illiquid, non-transparent positions. The challenge of security valuation facing the private equity world is the need to source pertinent and observable parametric data and this is why the Boyd model is an important additional to the modelling world.

References

This article "Boyd model" is from Wikipedia. The list of its authors can be seen in its historical. Articles copied from Draft Namespace on Wikipedia could be seen on the Draft Namespace of Wikipedia and not main one.

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