Financial Models for Predicting Price Movement Using Interest Rates

Vasicek model is a model used in finance that depicts the development, movement or evolution of interest rates. The model is based on one single factor or source of market risk but it is useful in evaluating the pricing of derivatives or interest rates. Developed in 1977 by Oldrich Vasicek, the model also has a function in stochastic charting (Vasicek, 1977). Vasicek himself characterized it as an equilibrium within the term structure. The formula for the model is and shows that stochastic differential equation gives place to the instant interest rate.

It is the parameter of the standard deviation that allows for volatility to be determined (James, Webber, 2000). Vasicek (1977) notes that a number of assumptions are at play in this formula -- such as the idea that spot interest "follows a diffusion process" and that it is on the spot rate that "discount bond" prices are dependent; the final assumption that "the market is efficient" (p. 177) is perhaps the most dangerous one -- or the one that applies least in today's market of dark pools, high-frequency traders, spoofing, and market manipulation.

One must have a sense of how different today's market is from Vasicek's of nearly forty years ago. The mathematics may not have changed, but the assumptions need to be updated. The context for which the model was created was the notion that interest rates cannot go up or down forever and will in the long run, or over time, proceed within a limited range.

There is a "drift factor" along with the long-term equilibrium parameter that is meant to serve as the bar to which interest rates return -- but in today's world of "artificially low" interest rates, this bar may be subject to further examination, even if the interest rate stays at a constant, non-fluctuating state. What Vasicek did not foresee in his model is the real possibility of negative interest rates, as we have today in Europe.

However, a different model -- the Cox-Ingersoll-Ross model, along with others like the Black-Karsinski model, have attempted to take this deficiency into consideration, by noting that the drift factor takes over for the evolution of the rate as it nears zero and thus the rate drifts higher back in the direction of its natural equilibrium. But of course this model assumes that the natural equilibrium is attainable because it also is based on the same assumption as Vasicek's -- namely that the market is efficient.

A number of hedge funds would debate this assumption in today's world, as they more and more move to cash positions and watch from the sidelines as liquidity drops lower and talk of a rate hike has investors just as rattled as talk of a rate drop (to negative). In short, the market is kept in such a state of instability and imbalance through Fed teasing that efficiency and market are two words that some would suggest do not go together in today's era of trading.

Nonetheless, the major limitation of Vasicek's model is that it does not account for the possibility of negative interest rates which are in place in Europe and which are looming in the U.S.

The other major limitation is that it assumes the market will naturally return to a state of equilibrium over the long-run, an assumption which cannot really be tested except through limited assessment of the past -- but to assume that the market of the old world is at all anything like the market of the new world in the digital era is to potentially make a fatal mistake in the new order (Copeland, Weston, Shastri, 2005).

Improvements that could be brought to this model, therefore, have been made by the Hull-White model, which shows that interest rate movement is equal to bond option prices, caps and floors can be determined using the Hull-White model and swaptions can be priced/calibrated accordingly (Hull, White, 1996). In terms of short-term financial management parameters are estimated from empirical data and then fed into the model to provide a sense of how the market is moving.

While the examples provide a sense of how the model works with serving as long-term variance and the stochastic differential equation is solved by the formula there remains the problematic factor of historical trends shifting so radically in recent years, with the introduction of new, major players in making major market decisions, such as the ECB, that new models are needed to theorize the known unknowns.

But today's market is not without its market shocks and for the interest rate to remain constant for the drift factor to take the rate into positive territory, is to assume more than the market is willing to allow the model to do at this point (Svoboda, 2004). Nonetheless, its application is still relevant in terms of evaluating predictive factors judging nominal interest rates to always remain positive and for the drift flow to rise towards equilibrium when the rate gets closer to zero.

Thus, it is entirely possible that while the model serves some significance, the need to adopt a model that considers the effect of negative interest rates the nominal rate relationship to that instance is imperative for discerning a more effective model for what could potentially be a severe market shock if such announcement comes within the coming months or years (Lal, Ouoba, 2012).

The fact that interest rates today are controlled and manipulated by the Fed, with nonstop predictions of whether there will be more QE or perhaps zero- or even negative-interest rate policy to be enacted only serves to indicate the brave new world that is upon us as the market deteriorates into a giant bubble built on the buy-the-dip mentality of HFT day traders and market makers playing fast and loose with SEC/FINRA regulations regarding naked shorting, etc. In this era of mind-boggling digital advantages, the.