Автор: Kimuro
Forex barrier options
A knock-out option in which the barrier is in-the-money with respect to the strike is called a reverse knock-out option. A knock-in option in which the barrier is in-the-money with respect to the strike is called a reverse knock-in option. How do we make money with this position? For example, we would buy a cheap 1-month 1. Ideally, spot drifts higher very slowly, ending up just less than 1. We exercise the option, buying our US dollars against Canadian dollars at 1.
The higher the implied volatility at the time the option is priced, the cheaper the knock out option with the in-the-money trigger will be, compared to the similar plain vanilla option. Higher implied volatilities suggest a greater probability of triggering the barrier and knocking out the exotic options. The reverse is true of the reverse knock-in option. It will still be cheaper than the plain vanilla option, but not by very much. The higher the implied volatility, the less of a difference there will be in price between the reverse knock-in option and the corresponding plain vanilla option.
If we own a reverse knock-out option and a reverse knock-in option with the same maturity, strike, and trigger, holding the combined position is equivalent to owning the corresponding plain vanilla option. Barrier Option Management Managing reverse barrier exotic options can be a difficult proposition, especially if spot trades near the barrier as it gets close to maturity.
A double-barrier option is like a more complicated version of a reverse barrier option. The payoff of average rate options is calculated by taking the difference between the average for a pre-set index over the life of the option and the strike price and then multiplying this difference by the notional amount. Because an average of a spot price is less volatile than a spot price, average rate options are naturally cheaper than the corresponding vanilla options.
A lookback call gives the owner the right to buy the underlying at expiry at a strike price equal to the lowest price that spot traded over the life of the option. A lookback put gives the owner the right to sell the underlying at expiry at a strike price equal to the highest price that spot traded over the life of the option.
The payoff of lookback options depends on the best rate that spot traded over the life of the option. Lookbacks are expensive. Anything that gives you the right to pick the top or the bottom is going to be costly. As a general rule of thumb, some people like to think that lookback prices are in the ballpark if they are roughly twice the price of an at-the-money straddle.
These types of products are often used by corporations to hedge the foreign exchange risk involved with overseas acquisitions when the success of the acquisition itself is uncertain. So the trader will probably sell these excess shares below the barrier level and incurs a loss on this sale.
Clearly, the risks of a barrier option near the barrier level can be difficult to manage. The delta of a barrier option can jump near the barrier causing hedging problems. To make things worst, it actually changes sign around the barrier.
A long DIP position goes from being long gamma to short gamma as the share price approaches the barrier. One method to smooth out the risks to make them manageable is to apply a barrier shift. To avoid the loss of selling the excess shares below the barrier level, the trade will give himself a cushion.
To do that, he will price and risk manage a slightly different option where the barrier is shifted downwards in such a way that the trader has enough room to sell the excess shares without incurring a loss. It makes the option cheaper for the trader. The larger the size, the more shares will have to be sold over the barrier, therefore the trader is more likely to move the stock price against him.
To sum up, the larger the transaction size, the larger the barrier shift. The difference between strike price and barrier level. If this difference is large, the DIP goes from not being a put to a put that is far ITM when the underlying pruce breaches the barrier. To sum up, the larger the difference between strike price and barrier level, the larger the barrier shift. The daily volume of the underlying share.
If the daily traded volume is low, it might be difficult for the trader to sell the excess shares over the barrier and he will likely sell them at a bad price, incurring a higher loss. To sum up, the lower the daily traded volume of the underlying asset, the larger the barrier shift.
These three first factors form a liquidity-based barrier shift and account for the discontinuity in the Delta near the barrier. The volatility of the underlying stock. The more volatile the underlying stock, the large is the risk to the trader of the stock price approaching the barrier level. In other words, the larger the volatility, the larger the barrier shift needed to protect the trader against a larger move.
This can be easily seen through our previous example. You are the trader long It means that you need to be long a Well, you were long This kind of gap down can bring situations where the trader would actually need to buy stocks when the barrier is breached. At this point, the absolute delta is not particularly huge and the trader has not accumulate any excess delta.
If the stock price goes through the barrier in a gap move down, the absolute delta will increase and the trader will need to buy shares and will be able to do so at a lower pricer. The barrier level. Since lower stock prices tend to go hand in hand with higher volatilities and higher volatilities result in larger barrier shift, the lower the barrier level, the higher the barrier shift.
The time left to maturity. The closer to maturity, the larger the absolute delta just before the barrier and therefore the larger the change in delta over the barrier. This translates into a higher risk and a higher barrier shift for shorter maturities. Note that certain types of barrier options do not require a barrier shift. A long position in a UO put is a good example. The delta hedge of such position is always a long share position so that the trader will need to sell shares over the barrier.
The trader does not need to shift the barrier as he can always let a limit order just before the barrier. If the stock gaps up, he will be pretty happy to sell them at a higher price anyway. Until now, we have only considered constant barrier shift but the it could also be an increasing function of time.
It is quite intuitive if you think about it. In the first days of an option's life, under normal levels of volatility, it is quite unlikely to see the underlying breach the barrier level. If one were to simulate paths and monitor the points in time at which the barrier was breached, it is quite obvious that the KI events occur more frequently down the line.
That is the reason why traders often apply a barrier shift that is an increasing function of time. Trader 2 is less conservative and decides to apply a linear barrier shift. At inception date, there is no barrier shift since there is no expected risk around the barrier. Trader number 3 uses a curvy barrier shift in time which is computed from evaluating knock-in scenarios. Therefore, his bid is the highest and he wins the trade in this case. This is the case when barrier options are only live at maturity or on specific days.
However, barrier options that are only live at maturity can also be priced as a combination of European options. The tighter the put spread the more the replication converges to the actual price of the DIP with KI at maturity only. This is exactly the same here as the discontinuity around the barrier corresponds somehow to a digital option.
Now that you have seen how you can replicate a barrier option with barrier observation at maturity only, you should easily see why these barrier options are sensitive to skew! The trader buying a DIP is therefore long volatility. This long vega position can be hedged, at leat partially, by buying vaniall put options on the same underlying stock with strikes between the barrier and the spot.
Risk wise one can compare a KI barrier to a long option position at that barrier and a KO option to a short option position at the specific barrier. It is clear then that the owner of DIP is long the skew as his position is similar to being long a downside option option with lower strike.
In the presence of skew, the volatility around the barrier is higher than the ATM volatility, which makes the probability of crossing the barrier higher. From a model point of view, we will need to calibrate a model to the IVs of options on the underlying asset across strikes with specific attention to the downside skew. If the barrier is monitored continuously, we will need a model that gives a smooth calibration through all ends of the surface between short maturities and up to the option's maturity.
It means we will need to calibrate to both skew and term structure. The reason is that a continuously monitored barrier option can be triggered at any time up to maturity, therefore it has vega sensitivity through the different time buckets.
So European options with different maturities must be calibrated so that the model shows risk against them. You must understand that the vega sensitivity will change as the underlying moves if the underlying stock gets closer to the barrier level, then the short term vega will increase and the long term vega will decrease.
CONSULTA DE SALDOS INTERBANK FOREX
Putting aside complicated models and math, let's take a look at some basic FX option setups that are used by both novice and experienced traders. Basic options strategies always start with plain vanilla options. This strategy is the easiest and simplest trade, with the trader buying an outright call or put option in order to express a directional view of the exchange rate.
Placing an outright or naked option position is one of the easiest strategies when it comes to FX options. We confirm this by the technical double top formation. This is a great time for a put option. An FX trader looking to short the Australian dollar against the U.
But in this case, the trade should be set to exit at 0. Preferred by traders, spread trades are a bit more complicated but they do become easier with practice. The first of these spread trades is the debit spread , also known as the bull call or bear put. Here, the trader is confident of the exchange rate's direction, but wants to play it a bit safer with a little less risk.
In the chart below, we see an But instead of paying out the premium, the currency option trader is looking to profit from the premium through the spread while maintaining a trade direction. This strategy is sometimes referred to as a bull put or bear call spread.
With support at Not only is the trader gaining from the option premium , but they are also avoiding the use of any real cash to implement it. Both sets of strategies are great for directional plays. Option Straddle So, what happens if the trader is neutral against the currency, but expects a short-term change in volatility? Similar to comparable equity options plays, currency traders will construct an option straddle strategy.
These are great trades for the FX portfolio in order to capture a potential breakout move or lulled pause in the exchange rate. The straddle is a bit simpler to set up compared to credit or debit spread trades. How big would that trade have to be? Would it have to be on an exchange or could it be between private parties? When barrier options were first introduced to options markets, many banks had legal trouble resulting from a mismatched understanding with their counterparties regarding exactly what constituted a barrier event.
Variations[ edit ] Barrier options are sometimes accompanied by a rebate, which is a payoff to the option holder in case of a barrier event. Rebates can either be paid at the time of the event or at expiration. A discrete barrier is one for which the barrier event is considered at discrete times, rather than the normal continuous barrier case. A Parisian option is a barrier option where the barrier condition applies only once the price of the underlying instrument has spent at least a given period of time on the wrong side of the barrier.
A turbo warrant is a barrier option namely a knock out call that is initially in the money and with the barrier at the same level as the strike. Barrier options can have either American , Bermudan or European exercise style. Valuation[ edit ] The valuation of barrier options can be tricky, because unlike other simpler options they are path-dependent — that is, the value of the option at any time depends not just on the underlying at that point, but also on the path taken by the underlying since, if it has crossed the barrier, a barrier event has occurred.
Although the classical Black—Scholes approach does not directly apply, several more complex methods can be used: The simplest way to value barrier options is to use a static replicating portfolio of vanilla options which can be valued with Black—Scholes , chosen so as to mimic the value of the barrier at expiry and at selected discrete points in time along the barrier. This approach was pioneered by Peter Carr and gives closed form prices and replication strategies for all types of barrier options, but usually only by assuming that the Black-Scholes model is correct.
This method is therefore inappropriate when there is a volatility smile.
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