4.5 Option.help

Octarisk Class: object = Option(id)

Octarisk Class: object = Option()

Class for setting up Option objects. Possible underlyings are financial instruments or indizes. Therefore the following Option types are introduced:

• OPT_EUR_C: European Call option priced by Black-Scholes model.
• OPT_EUR_P: European Put option priced by Black-Scholes model.
• OPT_AM_C: American Call option priced by Willow tree model, CRR binomial tree or Bjerksund-Stensland approximation.
• OPT_AM_P: European Put option priced by Willow tree model, CRR binomial tree or Bjerksund-Stensland approximation.
• OPT_BAR_C: European Barrier Call option. Can have all combinations of out or in and up or down barrier types. Priced with Merton, Reiner, Rubinstein model.
• OPT_BAR_P: European Barrier Put option. Same restrictions as Barrier Call options.
• OPT_ASN_C: European Asian Call option. Average rate only. The following compounding types can be used: geometric continuous (Kemna-Vorst90 pricing model) or arithmetic continuous (Levy pricing model)
• OPT_ASN_P: European Asian Put option. Same restrictions as Asian Call options.
• OPT_BIN_C: European Binary Call option. Binary types gap, supershare, asset-or-nothing or cash-or-nothing. Priced with Reiner-Rubinstein model.
• OPT_BIN_P: European Binary Put option. Same restrictions as Binary Call options.
• OPT_LBK_C: European Lookback Call option. Lookback types floating_strike or fixed_strike. Priced with Conze and Viswanathan or Goldman, Sosin and Gatto model.
• OPT_LBP_P: European Lookback Put option. Same restrictions as Lookback Call options.

In the following, all methods and attributes are explained and a code example is given.

Methods for Option object obj:

• Option(id) or Option(): Constructor of a Option object. id is optional and specifies id and name of new object.
• obj.set(attribute,value): Setter method. Provide pairs of attributes and values. Values are checked for format and constraints.
• obj.get(attribute): Getter method. Query the value of specified attribute.
• obj.calc_value(valuation_date,scenario, underlying, discount_curve, volatility_surface, path_static) Calculate the value of Options based on valuation date, scenario type, discount curve, underlying instrument and volatility surface. The pricing model is chosen based on Option type and instrument model attributes. A path to precalculated Willow trees for pricing American options by Willowtree model can be provided.
• obj.calc_greeks(valuation_date,scenario, underlying, discount_curve, volatility_surface, path_static) Calculate sensitivities (the Greeks) for the given Option instrument. For plain-vanilla European Options the Greeks are calculated by Black-Scholes pricing. The Greeks of all other Option types will be calculated by numeric approximation.
• obj.calc_vola_spread(valuation_date, underlying, discount_curve, volatility_surface, path_static) Calibrate volatility spread in order to match the Option price with the market price. The volatility spread will be used for further pricing.
• obj.getValue(scenario): Return Option value for given scenario. Method inherited from Superclass Instrument
• Option.help(format,returnflag): show this message. Format can be [plain text, html or texinfo]. If empty, defaults to plain text. Returnflag is boolean: True returns documentation string, false (default) returns empty string. [static method]

Attributes of Option objects:

• id: Instrument id. Has to be unique identifier. (Default: empty string)
• name: Instrument name. (Default: empty string)
• description: Instrument description. (Default: empty string)
• value_base: Base value of instrument of type real numeric. (Default: 0.0)
• currency: Currency of instrument of type string. (Default: ’EUR’) During instrument valuation and aggregation, FX conversion takes place if corresponding FX rate is available.
• asset_class: Asset class of instrument. (Default: ’derivative’)
• type: Type of instrument, specific for class. Set to ’Option’.
• value_stress: Line vector with instrument stress scenario values.
• value_mc: Line vector with instrument scenario values. MC values for several timestep_mc are stored in columns.
• timestep_mc: String Cell array with MC timesteps. If new timesteps are set, values are automatically appended.
• maturity_date: Maturity date of Option (date in format DD-MMM-YYYY)
• day_count_convention: Day count convention of curve. See ’help get_basis’ for details (Default: ’act/365’)
• compounding_type: Compounding type. Can be continuous, discrete or simple. (Default: ’cont’)
• compounding_freq: Compounding frequency used for discrete compounding. Can be [daily, weekly, monthly, quarterly, semi-annual, annual]. (Default: ’annual’)
• spread: Interest rate spread used in calculating risk free interest rate. Default: 0.0;
• discount_curve: ID of discount curve. Default: empty string
• underlying: ID of underlying object (instrument or risk factor). Default: empty string
• vola_surface: ID of volatility surface. Default: empty string
• vola_sensi: Sensitivity scaling factor for volatility. Default: 1
• strike: Strike value of Option (used to set maximum and minimum values for lookback options). Default: 100
• spot: Spot value of underlying instrment. Only used, if underlying is risk factor.
• multiplier: Multiplier of Option. Resulting Option price is scales by this multiplier. Default: 5
• div_yield: Continuous dividend yield of underlying (act/365 day count convention assumed). Default: 0.0
• timesteps_size: American Willow Tree timestep size (in days). Default: 5
• willowtree_nodes: American Willow Tree nodes per timestep. Default: 20
• pricing_function_american: American pricing model [Willowtree,BjSten]. Default: ’BjSten’
• binary_type: Binary option type. Can be [’cash’,’gap’,’asset’,’supershare’]. Defaults to ’cash’.
• lookback_type: Lookback option type. Can be [’floating_strike’,’fixed_strike’]. Defaults to ’floating_strike’.
• payoff_strike: Binary Option payoff strike (used as e.g. upper bound or strike). Default: 100
• upordown: Barrier Up or Down description. Default: ’U’
• outorin: Barrier In or Out description. Default: ’out’
• barrierlevel: Barrier level. Default: 0.0
• rebate: Barrier rebate (payoff in case of a barrier event). Default: 0.0
• averaging_type Asian option averaging type [’rate’,’strike’]. Defaults to ’rate’.
• averaging_rule = Asian option underlying distribution of average type [’geometric’,’arithmetic’]. Defaults to ’geometric’
• averaging_monitoring Asian option average monitoring. Can only be ’continuous’
• theo_delta: Sensitivity to changes in underlying’s price. Calculate by method calc_greeks.
• theo_gamma: Sensitivity to changes in changes of underlying’s price. Calculate by method calc_greeks.
• theo_vega: Sensitivity to changes in volatility. Calculate by method calc_greeks.
• theo_theta: Sensitivity to changes in remaining days to maturity. Calculate by method calc_greeks.
• theo_rho: Sensitivity to changes in risk free rate. Calculate by method calc_greeks.
• theo_omega: Specified as theo_delta scaled by underlying value over option base value. Calculate by method calc_greeks.

For illustration see the following example: An American equity Option with 10 years to maturity, an underlying index, a volatility surface and a discount curve are set up and the Option value (123.043), volatility spread and the Greeks are calculated by the Willowtree model and retrieved:

disp('Pricing American Option Object (Willowtree)')
c = Curve();
c = c.set('id','IR_EUR','nodes',[730,3650,4380], ...
'rates_base',[0.0001001034,0.0045624391,0.0062559362], ...
'method_interpolation','linear');
v = Surface();
v = v.set('axis_x',3650,'axis_x_name','TERM','axis_y',1.1, ...
'axis_y_name','MONEYNESS');
v = v.set('values_base',0.210360082233);
v = v.set('type','IndexVol');
i = Index();
i = i.set('value_base',286.867623322,'currency','USD');
o = Option();
o = o.set('maturity_date','29-Mar-2026','currency','USD', ...
'timesteps_size',5,'willowtree_nodes',30);
o = o.set('strike',368.7362,'multiplier',1,'sub_Type','OPT_AM_P');
o = o.set('pricing_function_american','Willowtree');
o = o.calc_value('31-Mar-2016','base',i,c,v);
o = o.calc_greeks('31-Mar-2016','base',i,c,v);
value_base = o.getValue('base')
theo_omega = o.get('theo_omega')
disp('Calibrating volatility spread over yield:')
o = o.set('value_base',100);
o = o.calc_vola_spread('31-Mar-2016',i,c,v);
o.getValue('base')

Dependencies of class: