To approximate the number of transactions based on volatility you will need to make many simulations and run your trading strategy in all the simulations and then take the average or the median as an approximation. To make the simulations you can use the Random Walk approach.
You can use GBM equation to create a Random walk simulation as shown below:
A Geometric Brownian motion (GBM) (also known as exponential Brownian motion) is a continuous-time stochastic process in which the logarithm of the randomly varying quantity follows a Brownian motion (also called a Wiener process) with drift.
To simulate the stock prices we can use the SDE or Stochastic Differential Equation of St (a stochastic process).
SDE===> dSt = 𝛍St dt + 𝞼St dWt
St is a stochastic process
𝛍 is the percentage drift
𝞼 is the percentage of volatility
Wt is a Weiner’s process or Brownian motion
If you want to link this equation to a stock data then you can think of St as the stock price at time step t, 𝛍 as the average daily return and 𝞼 as the average daily volatility of the stock. Let us try to simulate the stock prices from the above equation by expanding it further using the Ito’s interpretation.
St = St-1* exp((𝛍-(𝞼^2/2))*t + 𝞼*Wt)
St is stock price at time t
St-1 is stock price at time t-1
𝛍 is the mean daily returns
𝞼 is the mean daily volatility
t is the time interval of the step
Wt is random normal noise
These simulations are very useful when one is interested in finding the VaR or the expected shortfall for a particular stock with a certain degree of confidence. This exactly what your question is. To calculate the VaR you just need to take the lower x% percentile price(p) of all the simulated prices. This should give you the confidence-x and price p associated with it. For a given confidence value, you can get the price associated with it.