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����,,Pricing of a barrier optionspot44Price/value of the underlying assetvol::Annual volatility of the underlying assetr88Interest rate (continuously compounded)rf	@@Foreign interest rate (continuously compounded)
T88Time to maturity of the option in yearsstrike
,,Strike level of the optionbarrier_low>>Lower barrier (set to 0 for no lower barrier)barrier_up>>Upper barrier (set to 0 for no upper barrier)rebateDDAmount of money paid at maturity if barrier was hitput/callFFString to define if the option is a (p)ut or a (c)allknock in/outTTString to define if the option is of type knock-(i)n or knock-(o)utbarrier_typennString to define whether the barrier is observed (c)ontinuously or only at the (e)nd/maturitygreekOptional parameter, if left out then the function simply returns the option price; if set, the function returns price sensitivities (Greeks) to one of the input parameters; possible values are (d)elta, (g)amma, (t)heta, v(e)ga, v(o)lga, v(a)nna, (r)ho, rho(f)�f44Pricing of a touch/no-touch optionspot44Price/value of the underlying assetvol::Annual volatility of the underlying assetr88Interest rate (continuously compounded)rf	@@Foreign interest rate (continuously compounded)
T88Time to maturity of the option in yearsbarrier_low
>>Lower barrier (set to 0 for no lower barrier)barrier_up>>Upper barrier (set to 0 for no upper barrier)""foreign/domestic��String to define if the option pays one unit of (d)omestic currency (cash or nothing) or (f)oreign currency (asset or nothing)knock in/outhhString to define if the option is of type knock-(i)n (touch) or knock-(o)ut (no-touch)barrier_typennString to define whether the barrier is observed (c)ontinuously or only at the (e)nd/maturitygreekOptional parameter, if left out then the function simply returns the option price; if set, the function returns price sensitivities (Greeks) to one of the input parameters; possible values are (d)elta, (g)amma, (t)heta, v(e)ga, v(o)lga, v(a)nna, (r)ho, rho(f)�BddProbability that an asset hits a barrier assuming it follows dS/S = mu dt + vol dWspot66Price/value S of the underlying assetvol::Annual volatility of the underlying assetdrift66Parameter mu in dS/S = mu dt + vol dWT	""Time to maturity
barrier_low>>Lower barrier (set to 0 for no lower barrier)barrier_up
>>Upper barrier (set to 0 for no upper barrier)��LLProbability that an asset will at maturity end up between two barrier levels, assuming it follows dS/S = mu dt + vol dW (if the last two optional parameters (strike, put/call) are specified, the probability of S_T in [strike, upper barrier] for a call and S_T in [lower barrier, strike] for a put will be returned)spot**Price/value of the assetvol00Annual volatility of the assetdrift88Parameter mu from dS/S = mu dt + vol dWT	**Time to maturity in years
barrier_low>>Lower barrier (set to 0 for no lower barrier)barrier_up
>>Upper barrier (set to 0 for no upper barrier)put/call00Optional (p)ut/(c)all indicatorstrike&&Optional strike level���OPT_BARRIER�OPT_TOUCH�OPT_PROB_HIT�""OPT_PROB_INMONEY���y$$OPT_BARRIER�y""OPT_TOUCH�y&&OPT_PROB_HIT�y**OPT_PROB_INMONEY��"����|4