# Tag Info

8

This is in fact a tricky matter. As you say one way is to calculate delta by an analytic formula, i.e. calculate the first derivative of the option pricing formula you are using with respect to the underlying's spot price. The second way is to do it numerically, i.e. change the spot price by a small value $dS$, calculate the value of the option and then ...

7

I assume you mean that the hedge error should go to zero when the time-step size goes to zero. This is the case! I have a BS delta hedge simulator here: http://www.christian-fries.de/finmath/applets/HedgeSimulator.html and the source code here: http://www.finmath.net/java/ which shows that the delta hedge converges. However, in order to have that result, ...

4

First when transaction costs are involved the trader has to make a tradeoff between return and risk. Continuous rebalancing/hedging could lead to infinite transaction costs but provides (in theory) a perfect hedge. Discrete hedging enables to minimize transaticton cost but leads to hedgint errors and more risk. To find a price one must introduce an ...

3

I think you need to go even one step further than vonjd went in his reply. If liquid trading of the underlying is not possible, not only the arbitrage argument underlying risk neutral pricing breaks down. In that case there is simply no reason why the prices of those two assets (the option and its underlying) should be related in any way at all. So in my ...

3

Assuming you already have a way to obtain hedge ratios and the like, your best available choice is probably blotter (used to be just quantstrat). You will find that it isn't necessarily oriented toward options. Generally for options backtesting, pros end up making their own or buying commercial software. There are tons of commercial providers, but I ...

2

I think you incorrectly calculate portfolio values. For me the easiest way to keep track of portfolio positions and avg price is to separately calculate the sum of volume traded on the long and short side and to also calculate an average price separately for buys and sells. You obviously must update the avg price and size of the particular side ...

2

It may be the case with certain exotics that greeks are derived analytically through approximations. In that case at certain boundaries you may get different results from such approximation over the numerical approach. Why do you not approach the numerical case similarly than most banks and hedge funds when they "shock" their options books: Simply shift your ...

2

Calendar spreads have a number of disadvantages for trading Vega: Vega in different months are generally not additive, some traders use root-time-Vega but it does not remove the additional risk. You are trading time spread not just volatility, so be careful Calendar spreads are affected by dividends and rate changes - another source of risk. A ...

2

"does the underlying usually see increased trading?" Not necessarily. Most market makers do not re-hedge much in the underlying. In many markets the delta is exchanged (off-exchange) alongside the options trade at initiation, making both parties delta neutral at the outset. Re-hedges in large vol books are generally accomplished through other options and ...

1

You can formulate the problem of finding the optimal hedging frequency under transaction costs to maximize the Sharpe ratio of the delta-hedging strategy. The risk is the P&L volatility and the reward is smaller transaction costs. Analytical solutions and similar analysis can also be applied to spot- and delta-based hedging strategies. Details in ...

1

You can construct delta and gamma neutral option portfolio, but: It won't generally stay neutral forever, so you would still have to constantly rebalance it by trading additional options (thus paying more transaction costs and creating mess in the portofolio). Anything will break the neutrality - underlying move, time passage, implied volatility change ...

1

Lets give it a rough go then. Two assumptions. (1) We disregard repo (to lend the stock you may want to short) or financing on your hedged position. And (2) We assume no trading of the gamma on the option. Then I would assume the break-even is equal to the expiry should be equal to... (CALL) paidPremium/(1-hedgedDelta) + callStrike (PUT) putStrike - ...

1

My first thought would be to use quantlib package to get the delta values and comply those to get a position delta. Then use rules based on delta values to hedge. Use discrete time adjustments or use delta bands.

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