Asian options and C++/Quantlib
4 stars based on
MC can be used to value products for which an analytical price is not available in a given model, which includes most exotic derivatives in most models. The insight in the control variate technique is to use the knowledge given to us by the control variate to reduce this error. The textbook example is the Asian Option. Although the arithmetic version of the asian option discussed in previous posts has no analytic expression in BS, a similar Geometric asian option does have an analytic price.
So, for a given set of model parameters, we can calculate the price of the option. As a reminder, the payoff of an arithmetic asian option at expiry is.
Using as a control variate, we instead calculate. What do we gain from this? Well, consider the variance of. Consequently, we expect to see a reduction in variance of about times for a given number of paths although we now have to do a little more work on each path, as we need to calculate the geometric average as well as the arithmetic average of spots.
We saw that it was exotic — it is not possible to give it a unique price using only the information available from the asian option monte carlo c++. This option is similar, but its payoff is now based on the geometric average, rather than the arithmetic average, of the spot over the averaging dates.
This option is exotic, just like the regular arithmetic-average asian option. Further, since an arithmetic average is ALWAYS higher than a geometric average for a set of numbers, the price of the geometric asian will give us a strict lower bound on the price of the arithmetic asian.
This is just the same as the vanilla pricing problem solved here. So, we can use a vanilla pricer to asian option monte carlo c++ a geometric asian with two averaging dates, but we need to enter transformed parameters.
In fact this result is quite general, we can price a geometric asian with any number asian option monte carlo c++ averaging dates, using the general transformations below have a go at asian option monte carlo c++ this following the logic above.
In a recent post, I introduced Asian optionsan exotic option which pay the average of the underlying over a sequence of fixing dates. One subtlety is that we can no longer input a single expiry date, we now need an array of dates as our function input. This array can be entered as a row or column of excel cells, and should be the dates, expressed as years from the present date, to average over.
The simplest form of Asian option has asian option monte carlo c++ payoff similar to a vanilla option, but instead of depending on the value asian option monte carlo c++ the underlying spot price at expiry, it instead depends on the average the underlying spot price over a series of dates specified in the option contract. That is, the value of the option at expiry is the payoff. First of all, what does it mean that this is an exotic option?
From the market, we will be able to see the prices of vanilla options at or near each of the dates that the contract depends on. The answer, unfortunately, is no. The price at expiry will be. To calculate the price at earlier times, we use the martingale property of the discounted price in the risk-neutral measure.
We know from basic statistics that. What is this telling us? There are a binare optionen demokonto ohne anmeldung bdswiss of models that will all re-create the same vanilla prices, but will disagree on the price of anything more exotic, including our simple Asian option.
However, observed vanilla prices do allow us to put some bounds on the price of the option. For example, a careful application of the triangle inequality tells us that. In order to go further, we asian option monte carlo c++ to make a choice of model. Finally, a brief note on the naming and usage of Asian options. More exotic Asians might average over the last day of a month for a year. The relationship between payout for a geometric and an arithmetic asian option, which here demonstrate a So, we can use a vanilla pricer to price a geometric asian with two averaging dates, but we need to enter transformed parameters In fact this result is quite general, we can price a geometric asian with any number of averaging dates, using the general transformations below have a go at demonstrating this following the logic above.