Time-Independent Pricing of Options in Range Bound Markets

Abstract

Assuming that price of the underlying stock is moving in range bound, the Black-Scholes formula for options pricing supports a separation of variables. The resulting time-independent equation is solved employing different behavior of the option price function and three significant results are deduced. The first is the probability of stock price penetration through support or resistance level, called transmission coefficient. The second is the distance that price will go through once stock price penetrates out of the range bound. The last one is a predicted short time dramatic fall in the stock volatility right ahead of price tunneling. All three results are useful tools that give market practitioners valuable insights in choosing the right time to get involved in an option contract, about how far the price will go in case of a breakout, and how to correctly interpret volatility downfalls. JEL Classification: G13, G17.

Quantum Tunneling of Stock Price in Range Bound Market Conditions

“…From the time-dependent equation (9) it is stated in [1] that constant must have the form: (11) Inserting this result in the time-independent equation (10), the equation (1) is recovered.…”

“…In the recent article [1] it is recommended a time-independent equation to model the valuation of options having the underlying stock price moving in range bound. The equation in cause is identical to the one-dimensional time-independent Schrodinger equation having incorporated elements of finance and can be written as:…”

“…Setting the value of the right had term is mainly intuitively and is based on assessments of market and macroeconomic factors affecting option price in time. The extended discussion in finding 𝝺 values can be found in [1]. Here I will briefly sketch the main results to have the image of the process prior to explain the tunneling effect.…”

“…From the time-dependent equation ( 9) it is stated in [1] that 𝝺 constant must have the form: (11) Inserting this result in the time-independent equation (10), the equation ( 1) is recovered. This financial time-independent equation form the basis of stock price analysis exactly in the same manner time-independent Schrodinger equation serves the quantum particle physics.…”

“…Considering pricing the options having as underlying support stocks subjected to a range bound market a time-independent equation was recently deduced [1]. The equation is identical to the onedimensional time-independent Schrodinger equation but have financial elements incorporated.…”