The VMarket applet is a pedagogical tool showing how the price of financial derivatives can be calculated using a variety of different methods. Tag modifiers define the default behaviour of an applet: the selectors on the top of the applet switch between different types of simulations and the parameters on the right attribute specific values.

Execute.
Press the Start / Stop button to execute the VMarket applet until the value of the Time reaches the value RunTime or Step 1 to take unit steps of a duration TimeStep. Different functions are evolved (depending on the simulation) and are displayed in the plot window; approximative measurements can be read from the browser status bar after clicking in the plot window and are also printed to the Java console. Far more accuracy can be obtained by pressing the Print Console button and by reading the numerical output from the Java console:

• i is the index labeling the discrete representation of the solution.
• x[i] is the coordinate on the horizontal axis and can either be a spot price S or a spot rate r. In stock option calculations, x[i] measures the current market value of the underlying share S and is also called spot price. In credit market calculations, x[i] reprensents the current value of the short term interest rate r and is also called the spot rate.
• f0[i] (curve in grey) has completely different meanings depending on the simulation. In stock option calculations, f0[i] simply reminds the terminal payoff V(S) i.e. the value of the option on the expiry date. In bond market calculations, f0[i] displays the forecast yield as a function of time Y(t), this for a chosen value of the parameter SpotRate. Rather than reading the horizontal axis with x[i] as for the other curves, the time has to be computed manually using the variable index and the rule t=i*RunTime/MeshPoints
• f[i] (curve in black) is the main result of the calculation and displays the present value of the option, the discount function or the swap.
• g[i] (curve in blue) is not always present. In calculations involving barriers, g[i] shows the price of a vanilla option without the barrier feature. In bond market calculations, g[i] shows the yield that is simply obtained from the discount function with g[i]=-log(f[i])/time.

Selectors.
The selectors appearing on the top of VMarket applet define the type of problem. They are initialized with default values and are later modified to fit the values specified in the Tag window. Careful, white spaces count!

• topic selects the type of the financial product. Choices include
  "StckOption" (stock market options), "ZeroCpBond" (discount function), "BondOption" (bond market options), "IRateSwap" (interest rate swaps), "CreditModel" (credit market models), "RandomWalk" (generic Brownian motion), "Exercise" (programming assignments).
• method selects the numerical method. Choices include
  "FinDifferen" (finite differences), "FinElements" (finite elements), "Monte-Carlo" (without displaying walkers), "Monte-Carlo*" (with display of walkers), "DistribFct" (distribution without walkers), "DistribFct*" (distribution with walkers).
• scheme selects the flavour of a given product and method. Choices include
  "European" (using financial variables), "European logn" (using log-normal varables), "American" (using financial variables), "American logn" (using log-normal varables), "inBarrier" (in-barrier option), "outBarrier" (out-barrier option), "particles" (generic random walker), "Exercise 1.01" (all those that exist).
• ic selects the type of initial or terminal condition. Choices include
  "Put" (vanilla), "Call" (vanilla), "VSpread" (vertical spread), "SuperShr" (super share), "Discount" (discount function), "Gaussian" (distribution).

Run parameters.
The parameters appearing in a list on the right side of the VMarket applet are initialized with default values and are later modified to fit the values specified in the Tag window. They can be modified even later at run time by double-clicking the names. Note that only the parameters specified in the list of Tag modifiers (thought to be relevant) are listed. For a complete list at run-time, switch the selector from Double click below to Show all parameters.

• RunTime the run time T [years], e.g. 0.25 for 3 months
• Drift the relative total drift of the underlying m [1/year], e.g. 0.05 for a 5% annual drift
• Volatility the relative volatility of the underlying s [1/year], e.g. 0.5 for a 50% annual volatility
• LogNkappa exponent k in the random walk, e.g. 1=log-normal, 0=normal, 0.5=between
• SpotRate the short term interest (risk free, spot) rate r [1/year], e.g. 0.03 for a 3% annual risk free rate
• Dividend continuous dividend yield D₀ [1/years], e.g. 0.04 for a 4% continuous dividend payment
• StrikePrice the option exercise price at expiry K [currency], e.g. 10 for EUR 10
• MktPriceRsk market price of risk l, e.g. -0.5 for risk averse market
• MeanRevTarg target of mean reversion rate b, e.g. 0.05 for a 5% long term interest rate
• MeanRevVelo time scale of mean reversion process a, e.g. 2 for 1/2 year
• Shape0 shape parameter or amplitude, e.g. 1 for a Gaussian of unit height
• Shape1 shape parameter or position, e.g. 0 for a Gaussian centered on the origin
• Shape2 shape parameter or width, e.g. 1 for a Gaussian of unit width
• MeshLeft the lower end of the simulation range [currency or rate], e.g. 0 for an underlying share that can become worthless
• MeshLength the simulation range [currency or rate], e.g. 200 for an underlying share that may increase to 200 EUR during the RunTime
• MeshPoint the number of mesh points, e.g. 100 to calculate the price of a vanilla put option with an accuracy around 0.5%
• Walkers the number of random walkers, e.g. 1000 to calculate the price of a vanilla put option with an accuracy around 5%
• TimeStep the duration of one step [1/year], e.g. 0.00397 for one day, 0.01923 for one week
• TimeTheta the implicity parameter for time integration using FEM
• TuneQuad the tunable quadrature parameter using FEM
• UserInteger the user defined integer value
• UserDouble the user defined double value

HTML TAG modifiers format.
The VMarket applet is insearted in an HTML document via the Tag window using a header of the form

<applet codebase="$user_dir/applet/" code=vmarket 
    align=center width=780 height=420>
    <param name=topic               value="Exercise">
    <param name=scheme              value="Exercise 4.07">
    <param name=ic                  value="Put">
    <param name=method              value="FinDifferen">
    <param name=RunTime             value= 0.5>
    <param name=Drift               value= 0.1>
    <param name=Volatility          value= 0.4>
    <param name=LogNkappa           value= 1.>
    <param name=SpotRate            value= 0.1>
    <param name=Dividend            value= 0.>
    <param name=StrikePrice         value= 10.>
    <param name=Barrier             value= 0.>
    <param name=MktPriceRsk         value= 1.>
    <param name=MeanRevTarg         value= 0.05>
    <param name=MeanRevVelo         value= 0.1>
    <param name=Shape0              value= 6.>
    <param name=Shape1              value= 4.>
    <param name=Shape2              value=-2.>
    <param name=MeshLeft            value= 0.>
    <param name=MeshLength          value= 20.>
    <param name=MeshPoints          value= 100>
    <param name=Walkers             value= 300>
    <param name=TimeStep            value= 0.00397>
    <param name=TimeTheta           value= 0.7>
    <param name=TuneQuad            value= 0.333>
    <param name=UserInt             value= 0>
    <param name=UserDouble          value= 0.>
</applet>