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.

First check assignment 2.03 for a description of a market parametrized with a Drift=0.03, a Volatility=0.3, taking account of the price dynamics with a resistance / support level at Barrier=10.0 and an intensity UserDouble=0.02. A Monte-Carlo sampling of the underlying can now be used to calculate the expected value for a European put option with a StrikePrice=9.0 for up to 9 months or RunTime=0.75 years before the expiry and is discounted back to prevent time assuming a risk free SpotRate=0.03.

1. Study the payoff dynamics obtained with (UserInteger=2) and without (UserInteger=1) resistance / support level.
2. Click inside the plot area to measure the price in-the-money, at-the money and out-of-the money. Which option is is most affected?
3. Formulate a trading strategy exploiting the presence of a support level in the underlying, assuming that this has not already been priced into the derivatives market. Edit the parameters to acquire an intuition for the situations when such a strategy may exceed the transaction costs.

VMarket applet: press START/STOP for execution.

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 j=0; j<f.length; j++) {
    for(int k=0; k<numberOfRealisations; k++){
      currentState[k][j] += currentState[k][j] * 
        ( mu*timeStep +
          sigma*random.nextGaussian()*Math.sqrt(timeStep) );
    } // (for realisations)
  } // for (initial conditions)

} 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 j=0; j<f.length; j++) {

      // Insert her your code from assignment 2.03, substituting 
      //   currentState[k][0] -> currentState[k][j]

  } // for (initial conditions)

} // if (type)
        

Copyright © Doc Andre Jaun & Lifelong-Learners/opt at 06:53:57, May 05th, 2004