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Published byBranden Wheelwright Modified about 1 year ago

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An Innovative way of making options The Timer Option Gianni Baroncini Rocco Letterelli

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The first to study these options was Neuberger in 1990, also if he called them “mileage options”. Bick, in 1995, extended the analysis of such options to a continuous time setting. Timer Option Brief History In April 2007 Timer Options were introduced in the market for the first time by Société Générale Corporate and Investment Banking. In more recent times, , also Li, Bernard and Cui, have analyzed these options.

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Timer Option Main Characteristic The Investor is the decisional center The VolatilityThe Maturity He chooses

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Timer Option The variance budget The volatility and the maturity specified from the investor, are used to calculate the “Variance Budget” The product between target volatility squared and target maturity Once that the Variance Budget is consumed, the option expires. When realised volatility squared, multiplied by the number of expired days divided by 252, is greater than the Variance Budget The timer option expires if (σ^2) * (d/252) ≥ Variance Budget

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Timer Option

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Timer Option Payoff The payoff of a Timer Call or Timer Put, is similar to that of a Call or Put Timer Call (K) = max (S τ -K ; 0) Timer Put (K) = max (K- S τ ; 0) The difference with plain vanilla option is in τ, that it’s not known at t=0 Thus we can write that the price of a timer call option at time 0: E Q [e -r τ max (S τ - K ; 0)]

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Timer Option pricing:

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Timer option pricing MONTECARLO: We can simulate the joint path of the correlated processes (S t, V t ) to obtain n simulations of (T,S T ): We simulate V t+Δt and S t+Δt for each time step and we stop when V j reaches V V j is the accumulated variance at time j V is the variance budget Finally we record (j,S j ) as an approximation of (T,S T )

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Timer option pricing: Remarks: The smaller is Δt the better is the approximation of V t+Δt The main disavantage: implementation takes a long time We suppose ρ,r to be constant if r = 0 call 0 timer = call 0 B&S put 0 timer = put 0 B&S

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Timer Option Greeks However they can be expressed as expectations of the Greeks calculated in Black & Scholes model, using the target volatility and the target maturity specified by the investor in the model. The timer option, Greeks should be calculated in a numerical way. For instances, using numerical approximation, we can express the first derivative of our option as [f(x+Δx) – f(x – Δx)] / 2*Δx C 0 = E q [C bs (S 0,K, r, (V/τ)^0.5, τ)]

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Timer Option Applications (Speculate) Investors that have a strong expectation about the future stock price, and want to exploit it, should buy a Call (Put) Timer option when they belive that the implied volatility is greater respect to its effective volatility (in that case the plain vanilla is over-valued). A study that have analyzed all stocks in the Euro Stoxx 50 index from 2000 to 2007, calculates that 80% of three-month calls that have matured in-the-money were overpriced.

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Timer Option Applications (Stock Hedging) A Timer Option could be used also to hedge a stock position, exploiting the negative correlation that generally exists between stocks return and realized volatility. For instance, imagine that an investor wants to hedge himself against a collapse of the market, and for this reason he buys a Timer Put. If the market goes down, he is protected, and moreover this generally implies an increase in the realised volatility (his Timer Option will expiry sooner) On the contrary, in case of bullish market, that are usually markets with low realised volatility, the expiry date for the Timer Put will be longer respect to a simply Plain Vanilla Put. This means that, the investors cost for hedging will be lower, the need to roll the Timer Option is less frequent than for the Vanilla Option

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Timer Option Applications (Combination with a Plain Vanilla) Timer Options could be used also to create combination with Plain Vanilla Options: If we think that the implied volatility of the market is too high: buy a Timer Call sell a Plain Vanilla Call with same S and K (setting the Volatility Target below the implied volatility) At time t=0 The cost of the Timer Call is lower respect to the Plain Vanilla If we are right, timer call will expire later than plain vanilla Call thus: At time t=T we have plain Call= max(S T -k,0), timer Call= plain Call + time value If we are in a bullish market, the tenor of our Timer Option will be higher respect to the Plain Vanilla, and so we will capture the value due to the difference in time value of the two options.

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