2.03 Resistance and support levels

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2.03 Resistance and support levels

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Rather than showing a complete solution, the teacher decided here to give you his own applet and guide you through a series of experiments illustrating the effect of resistance / support levels. To complete this exercise, your task will be to implement your own scheme in the applet and discuss what you observe.

Examine first the evolution of prices in a market without resistance / support levels, simply by running the applet with the preset value UserInteger=1. Each red dot corresponds to a possible evolution starting from the current (spot) price S₀ chosen with StrikePrice=9.0 and evolves horizontally with a log-normal random walk here prescribed with a 6% Drift and a 30% Volatility. The black line accumulates the final realizations and can be understood as a probability density (or distribution function, vertical axis in per cent) of finding the future price in a unit interval (horizontal axis).

Observe how a simulation with 300 prices is rather noisy. Increase the number of Walkers to a value that still allows you to rapidly compute the 9 months evolution chosen with RunTime=0.75.

Switch from DistribFct* to DistribFct and repeat a calculation without displaying the prices. Describe the distribution function you obtain.

Press Toggle Display twice to re-normalize the plot and click inside the plot area to measure the coordinates. Relying a homogeneous mesh S_n = nh to integrate the area below the distribution P(S < S₀) = ò₀^S₀ p(S₀,0;S,T) dS » h(å_{n = 0}^N p(S_n) -[p(0)+p(N)]/2), you can calculate the probability that the price will drop during the time interval [0;T] of the simulation.

Now reload the default parameters and simulate the evolution of prices in a market with a resistance / support level by setting UserInteger=2.

Can you tell how the motion of each individual prices is affected? Discuss where and how the distribution function is altered.

Use the parameters Barrier and UserDouble to modify the position and the intensity of the resistance / support level.

Check the assignment 4.11 for a continuation of this problem in the context of option pricing.

VMarket applet: press START/STOP for execution.

Numerical scheme in Java:

double timeStep= runData.getParamValue("TimeStep"); // Run parameters
double mu      = runData.getParamValue("Drift");
double sigma   = runData.getParamValue("Volatility");
int    type    = runData.getParamValueInt("UserInteger");

if (type == 1) { // Log-normal walk for stock prices (no modification required)

  for(int k=0; k<numberOfRealisations; k++){
    currentState[k][0] += currentState[k][0] * 
        ( mu*timeStep +
          sigma*random.nextGaussian()*Math.sqrt(timeStep) );
  }

} else if (type == 2) { // Simulate resistance/support levels (please modify)

  double barrier   = runData.getParamValue("Barrier"); // Extra parameters
  double intensity = runData.getParamValue("UserDouble");
  double width     = 0.1*barrier;
  double odds      = 2*intensity-1; 

// Examples of useful functions in Java
// double uniform01  = Math.random();         // random number in U(0,1)
// double gaussian01 = random.nextGaussian(); // random number in N(0,1)
// double e   = Math.exp(1.);
// double one = Math.log(e);
// System.out.println("Debug: type="+type);   // print to browser Java-console

  for(int k=0; k<numberOfRealisations; k++){
    currentState[k][0] += currentState[k][0] * 
        ( mu*timeStep +
          sigma*random.nextGaussian()*Math.sqrt(timeStep) );
  }

} // if (type)

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