Exotic Derivatives Trading

February 19, 2009

Pricing Vol Flex – “Option to increase the Notional”

Filed under: Risk Management of Exotic Derivatives — Exotics Trader @ 3:27 pm

VolFlex: Client has the option to increase the notional at the traded price before the strike date of the option.

Utility: Imagine the situation of a retail bank that has come up with a new product and is not very sure about the sales figures it will be able to generate with that product. In such a case that bank would buy a Volflex- Buy the option on an initial notional of let’s say 30m and an option to increase the notional to 50m before the strike date. In cases where one is not sure of the net notional to trade go for a volflex.

Trade: A forward starting call on TOYOTA, with 3 months to strike date and 1 yr 3 months to maturity from now, Initial Notional 20m EUR, but the client has an option to increase the notional to 30M EUR in the next 3 months.


Client’s thought process/Structuring
Major growth driver for Toyota in terms of region: makes more than one-third of its sales in the US, So nearly one third of the earnings are in $’s.
Major factor influencing $/Yen rate: Carry trade, in which low-yielding currencies such as the yen are sold to finance purchases of riskier, higher-yielding assets elsewhere – primarily $’s
Information
Client knows that there is going to be a Fed meeting sometime in next 3 months, If Fed decides a rate cut, it will erode the dollar’s yield advantage against the yen. This will prompt investors to abandon carry trades & hence increasing the demand for Yen. This further implies that Toyota would get lesser Yens per dollar of sales in US. Now it is at this point of time, when a Client wishes to decrease the Notional on this trade. In case Fed decides to increase the rate, Client would be interested in increasing the Notional.

Pricing:
Price of a 3M forward starting 1 yr call TOYOTA is 7% (Notional 20m EUR). Now since the trader is giving the client an option to increase the Notional to 30m EUR (10/20 ~ 50% increase) at the same price of 7%, he needs to charge an extra premium for that.

What will be that premium?
Factors affecting the option’s price in next three months:
1. Volatility
2. Interest Rate

Delta ~ 0, Gamma~0 and vega is not a function of spot

Steps:

  1. Estimate the maximum change in volatility in the next 3 months. Considering the expected market conditions in the near future, mathematically it can be estimated by calculating the mean reversion rate and the mean volatility.
  2. (Estimated Change in Vol* Vega) is the maximum change in price that can occur due to change in Volatility.
    Current Vega: 40 bps, Estimated Vol change: 50 bps
    Expected change in price: 20 bps, trader is already risk managing the vega for a 20M EUR Notional, additional Vega to be hedged is for another 10M EUR (another 50%)
    So net Vega Premium: 50%*(Estimated Change in Vol* Vega) ~ 10 bps

Similarly we need to find the rho premium:
When traded as a note, i.e Client gives 100%, trader gives him an option worth x% and in return receives the EUR Libor on 100% + upfront

Traders/Note Seller’s net rho: Rho from Discounted Libor cash streams – Option rho ( We are short the note). Both can be easily estimated. Let’s assume that the net figure comes out to be 30 bps. i.e. if the EURO yield curve were to shift down by 1% a trader would lose 30 bps on this trade. The trader has hedged rho for a notional of 20 M but if the notional is increased to an extra 10 bucks, it gets worse for him.


Net rho risk to manage: 50%*30 bps ~ 15 bps
How to manage: Buy a swaption, i.e. option to swap (Fixed-Floating), As a buyer of the swaption, a trader can exercise it if he sees interest rates going down.

Estimate the cost of hedging the rho risk of 15 bps

The figure below shows EUR ATM Swaption straddles – Premium mids



Cost of 3M, 1 yr maturity swaption is 47 bps. Trader just wants to buy the put to hedge against the fall in interest rate, so net cost is 47/2 bps ~ 24 bps

Number of straddles to buy per notional: Net rho risk to manage/ Swaption Rho = 15 bps/3.8% ~ 0.0397 straddles,
Total Straddle Cost/Notional unit: 0.0397*24 bps ~ 1 bps

Net rho premium: Cost of hedging rho exposure incase client increases the notional by another 10 bucks: 1 bps

Net premium: rho premium + vega premium: 1 bps + 10 bps = 11 bps

Price Quoted by the trader: 11 bps + 7% ~ 7.11%

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1 Comment »

  1. agree with previous comments, great posts, just one comment on yen unwind should actually increase the demand for yen and hence cause a yen increase relative to usd

    Comment by Vladski — March 5, 2009 @ 10:19 pm | Reply


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