Hedging Strategies With Options - YouTube

Say that we have foreign exchange (forex / FX) exposure, what should we do to reduce the risk?

Let's say that the exporter wishes to sell USD in the upcoming future

Usually, it's common for exporters to reduce the forex risk by performing static hedge

Now what is a static hedge?

To exporters, the spot of USD/IDR = 14500 and 3-month FX forward = 14700 are good selling prices

In fact, selling USD at 14700 is already above their budget therefore they'll hedge by selling FX forward

So it is possible for them to do a static hedge or hedge and forget

Another way is to use FX option by (for instance) buying USD put / IDR call

As an alternative, we can also perform a combination of FX forwards and FX options

With FX forward, we can also do partial hedging

Here, the combination of FX forward and FX option can be seen on this graph

So, what's the difference between FX option and FX forward?

The FX forward contracts are a commitment; in which we've set a selling price at the time of our transaction

So whatever happens, we will sell USD with the price we agreed at the moment our transactions are done

If USD/IDR increases, there will be an opportunity loss

That's where option contract comes in

By using option, it is guaranteed that we are protected but we can still gain upside potential if the rate rises

If the rate dips below the strike price, we can still sell it at a strike price (14000) which is higher than the prevailing rate (13000)

On the contrary, if the rate goes up to 15000 we will for sure get a better selling price

So that's one of the many advantages of options; you get protection and still could gain upside potential

As we've discussed earlier, option transactions are non-linear instruments

Meanwhile, forward contracts and swaps are linear transactions

Linearity is much simpler because if the rate rises by 1%, we would get a 1% profit. Whereas if it goes down by 2%, we would get a 2% loss

That's why option needs a more sophisticated risk management

The most simple form of hedging for option portfolio is delta hedge

Delta for call option is the sensitivity of call option against the changes of spot or underlying

For instance, these dotted lines show the value of call option

The value of delta on this point is the first derivative of call against spot or the tangent on this very point

So with delta hedge, we estimate the value of option linearly with the help of this straight line

Of course, this estimate will be different with the correct value and the errors would get higher as changes in spot become bigger

For that reason, we need to add a second order which (in this case) is gamma or use delta-gamma hedge to reduce the error

Since delta is just a mere straight line whereas the estimation of delta-gamma uses a curved curve (quadratic function)

If we have a long call option, then the delta and gamma will be positive. Keep in mind that the value of gamma on long vanilla call or put option will always be positive

The value of delta for long put is negative

From this result, we can then perform hedging for delta, for instance

To hedge long call with a positive delta, we must find an instrument with a negative delta in order to get a zero delta

We can obtain negative delta by shorting FX spot or underlying such that the total delta is now equal to zero

We can't make gamma neutral by buying or selling the underlying, but we can do it using another option instead

The delta of short USD call / IDR put would approximately be equal to minus the change in call divided by the change in spot

We then hedge it by buying USD/IDR at the amount which is expected to offset the risk of the short USD call earlier

So that the value of the portfolio would be -c to pay the premium and the dc/dS multiplied by the current spot rate

With a change in spot in the amount of dS, therefore the change in portfolio value would most probably be equal to zero

Suppose we sold USD call / IDR put amounting USD 2 million with a delta of -0.5

Because the delta is -0.5 then it's as if we are selling USD/IDR with the amount of USD 1 million

We can then hedge it by buying USD/IDR amounting USD 1 million because buying USD/IDR would get a delta of 1 so that the total delta would now be equal to zero

Butterfly strategy, straddles and strangles are examples of delta neutral strategies

Unfortunately though, if we have delta neutral today, the next day the delta would not be zero due to spot or volatility changes

For example if the delta is equal to 40%, we must hedge the short USD call by buying USD/IDR with an amount of 40%

However, if the delta on the next day is 30%, we need to sell USD/IDR with the amount of 10% to keep the delta neutral

Hence we must perform rebalancing on delta hedging every day accordingly so that the total delta will always be around zero

Here is an example of how we could adjust the buy USD/IDR hedges every day for selling USD call / IDR put in order to not be exposed to the delta risk

Here's an example using data from the beginning of the year up until May 17, 2021 which shows that positive (-ve) values offset by another negative (+ve) values

The positive USD call will be offset by a negative long USD/IDR

That makes the value of the portfolio around zero; one at profit, the other one at loss and vice versa

But here the portfolio value is positive because it is assumed that there are no transaction cost

In reality, there will always be a hedging cost due to bid-offer spreads

By taking bid-offer spreads into account and after performing hedging repeatedly, the portfolio value will most likely be negative because of high hedging cost

One more thing, suppose we have a portfolio consisting of 4 OTC options with the given delta, gamma and vega

And an option traded with the given delta, gamma and vega like these

Another one that is traded with the assumed delta, gamma and vega like these

Three questions that need to be answered: how can we obtain a delta neutral, a delta-gamma neutral and a delta-gamma-vega neutral portfolios ?

Suppose I'm a FX option market maker that has these 4 options

So at the end of the day, how can we get our portfolio to be delta neutral, delta-gamma neutral or delta-gamma-vega neutral?

The first thing that we need to do is to calculate the total amount of delta, gamma and vega of our portfolio

The total delta is equal to 450, gamma is equal to 1050 and vega is equal to 2250

What should we do if the total delta is equal to 450?

Previously we know that short underlying has a delta of -1, so if we sell a 450 worth of underlying, the total delta will be zero (obtained from 450-450)

Up next we want our delta and gamma to be zero. We know that we can make delta neutral by buying or selling underlying

However we can't make gamma neutral or vega neutral using underlying because the gamma or vega of buying or selling underlying is equal to zero

So to make gamma nuetral, we need another option that has the opposite gamma

The sum of gamma of our portfolio is 1050, but the gamma of the first option is 0.3; what should we do to make the gamma of the first option equal to -1050 ?

What is X when multiplied by 0.3 is equal to -1050? The answer is X = -3500. So we need to sell the 1st option by -3050 such that the total gamma will be 1050 - 1050 = 0

However, with that option the delta of our portfolio would now be -1650. Hence, we must then also buy a 1650 worth of underlying to make the delta and gamma neutral

Unlike the previous scenario, we now need two options to make delta, gamma and vega neutral

If both options 1 and 2 are like these, to a get a zero gamma and vega, we need to make both of their columns zero by buying option 1(2) in the amount of w1(w2)

As a result, we would get these 2 equations

By using substitution method, we would get w2 = 750 and w1 = -4750

This means that we need to buy a 750 worth of option 2 and sell a 4750 worth of option 1, which would make the values of our gamma and vega to be equal to zero

But the delta is now equal to -2325 due to these two options

In order to make the delta, gamma and vega neutral, we need to buy an additional underlying worth of 2325

Any questions so far?