AMERICAN STYLE EXOTIC OPTIONS VALAUTION USING MONTE-CARLO SIMULATION

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1. Log into your account or if you are a new user, register your account and enable two factor authentication.
2. Click on the [American-style exotics] button, this will take you to the Dynamic-text-blocks parameters page.

Dynamic text-blocks parameters page

1. Select to enter pairwise-flat or pairwise-varying correlations between underlying share price variables.
2. Select the exotic option strategy to be valued from the following list:
   1. American-style rainbow option.
   2. American-style cash-or-nothing call option.
   3. American-style cash-or-nothing put option.
   4. American-style asset-or-nothing call option.
   5. American-style asset-or-nothing put option.
   6. European-style average-price call option.
   7. European-style average-price put option.
   8. American-style average-price call option.
   9. American-style average-price put option.
3. The European-style average-price options can also be valued using their respective analytic approximation pricing formulae and are included here mainly for model-accuracy-check by comparing model results with their analytic equivalents. The American-style raibow option is in general a super-set of various other options. Its general formulation is as follows: If S(1,j), S(2,j), S(3,j), ...., S(n,j) are share prices for n variables at time step j and K is the strike price, the expiry period(time step N) pay-off from the Rainbow option is MAX[a(1)*S(1,N)^(p(1)) + a(2)*S(2,N)^(p(2)) + a(3)*S(3,N)^(p(3)) + ... + a(n)*S(n,N)^(p(n)) - K,0], where MAX[V,0] is the maximum of V and zero, * is a symbol that represents multiplication, and ^ is a power operator. a(i) is the coefficient parameter for share variable S(i,j) and p(i) is its power parameter, the pay-off at exercise times j before maturity is MAX[MAX[a(1)*S(1,j)^(p(1)) + a(2)*S(2,j)^(p(2)) + a(3)*S(3,j)^(p(3)) + ... + a(n)*S(n,j)^(p(n)) - K,0],OP(j)], where OP(j) is the discounted price of the option price at time step j+1 if time period at time step j is greater than the vesting period, or OP(j) if it is less than the vesting period. The discount rate used is the forward interest rate applicable to the period between time-step j, and time-step j+1. The vesting period in this model is the period over which the option cannot be exercised which starts from current time and runs continuously till a specific time period. This formulation enables the American-style rainbow option to easily be customised to price a variety of American-style basket-options. This is the reason why a(i)'s and p(i)'s are collectively referred to as basket parameters. As an example, an American style vanilla put option can easily be valued as an American-style raibow option with one underlying share variable S(1) , and a(1) = -1, p(1) = 1, and K is set to a negative number, that is, if the strike price of the put option is 50, it should be entered in the system as -50. The-system uses an internal automatic calibrating weight parameter to make the prices of American-style options consistent with the prices one gets from using a binomial pricing approach although it is recommended to use the binomial-pricing-approach-application to price vanilla American-style options for efficiency reasons. The presence of the vesting period means the American-style rainbow option is a super-set of the European-style rainbow option. You can price a European-style rainbow option by setting the vesting period of its American-style equivalent to equal the option expiry period. The American style cash-or-nothing option is priced similarly and one gets the price of its European equivalent by setting the vesting period to equal expiry period. The European style avarage price options are priced by assuming exercise happens at maturity. The American-style average price options are priced by calculating the running average price and using the usual technique of testing whether the option is better dead or alive. The values of their European-style equivalents can be obtained by setting the respective vesting periods to equal their respective expiry periods.
4. Enter the option expiry in days. This system and model assumes that there are 365.25 days in a year and so you should multiply the expiry period in years by 365.25 to get its days-equivalent.
5. Select the number of time-steps to be used in Monte-Carlo simulation.
6. Click the submit button, and depending on the chosen option strategy you will be taken to either the array-populating-parameters page or array-populating page.

Array populating parameters page

1. You will be directed to this page if your chosen strategy requires you to enter the number of underlying share variables, that is, it is not internally chosen for you by the system.
2. Select the number of underlying share variables.
3. Click the submit button, and this will take you to the Array populating page.

Array populating page

1. Identifier indices used in this section start identification counting from 0, to make them consistent with programming of array indices.
2. Enter names of indicated underlying share price variables.
3. Enter number of discrete dividends before option expiry (enter zero if none) for indicated underlying share variable. Discrete dividend is, such that, if the underlying share price value just before dividend payment is S, and the value of discrete dividend is D, then the value of the share price just after discrete dividend payment is S-D.
4. Enter the number of known dividend yields before option expiry (enter zero if none) for indicated underlying share variable. Known dividend is, such that, if the underlying share price value just before dividend payment is S, and the value of known dividend yield is q, then the value of the share price just after dividend payment is S*(1-q).
5. If propmted, enter the coefficient parameters of indicated underlying share price variables.
6. If prompted, enter the power parameters of indicated underlying share price variables.
7. If prompted, enter the original expiry in days of the average price option at time of initial creation.
8. Enter pairwise correlations between indicated underlying share price variables.
9. Click the submit button, and this will take you to the American-style exotics valuation parameters page.

American-style exotics valuation parameters page

1. Enter the currency of valuation.
2. Enter option strike price.
3. Enter allocated expenses and tax to be added to the pure option price.
4. Enter profit percentage to be loaded to the calculated sum of pure option price and dealing expenses and tax. If the profit loading is x and the sum of pure option price plus expenses and tax is P, then the final price will be calculated as (1 + x)*P.It is important to note that valuation is done from a dealer/broker's perspective. The profit-charge is charged by the dealer/broker.
5. If prompted, enter vesting period in years.
6. If prompted, enter cash-or-nothing option contingent cash payment.
7. If prompted, enter past average price excluding current price that lies within option contract boundary.
8. Enter the initial prices of indicated share price variables.
9. Enter the continously compounded dividend yields of indicated share price variables. The continously compounded dividend yields together with discrete dividends, and known dividend yields, enable any dividend payment patterns to be accomodated in the pricing model.
10. Enter the annualised volatilities of indicated share price variables.
11. Enter discrete dividend values and their timing (this time in years not days like in other sections, divide by 365.25 for coversion from days to years) for indicated underlying share price variables.
12. Enter known dividend yield values and their timing (this time in years not days like in other sections, divide by 365.25 for coversion from days to years) for indicated underlying share price variables.
13. Click the submit button and this will take you to the output display page.

Output display page

1. You can view pricing model output together with input parameters you entered.
2. At the bottom of the page you can click on the button to create database record for the current model output. This will take you to the create database record page where you should click on the create button to create the database record.
3. After clicking on the create button to create the database record, you will be taken to the database records view page, where you can scroll vertically or horizontally to view database records including the one you just created.
4. You can filter database records according to the currency of valuation using the filter box. You can click on the details link on the extreme right of a particular database record, this will take you to the particular database record details page.
5. Click on the graph plot link to display longitudinal graph plots for the option price distibution parameters. You can also choose to view cross-sectional graph plots. These tend to show very high frequency at time zero and relatively small frequencies at values above zero. This is consistent with the option pay-off structure.