October 10th, 2015, 6:50 am
QuoteOriginally posted by: crmorcomThis is a fairly useful exercise, but is still simulated. Worth also looking at actual backtests - particularly because it looks like this paper has fixed vols and no vega effects, which are rather important.The paper provides analytical (approximate) formulas for the expected P&L, transaction costs, and P&L volatility for the log-normal price dynamics which may include jumps and stochastic volatility. The hedging can be deterministic at fixed time steps or range based with triggers from either changes in price or delta. Monte-Carlo simulations are only applied to verify these approximate formulas and show that these formulas are indeed accurate. An assumption is made that the option is delta-hedged to maturity so that the vega, while important for day-to-day P&L, has no impact on the terminal P&L from the delta-hedge.QuoteOriginally posted by: crmorcomYou'll notice that, if you cast a quick eye over the time-based hedging tables at the end, that once a day is not far from optimal for all the models and, within a range of hedging frequencies near optimal, most of the time you don't make a huge difference to your SR.If you look at Figures 1 and 2 in the paper above, you can see that the Sharpe ratio of the delta-hedging strategy has a humped shape as a function of the hedging frequency. On the one hand, when you hedge infrequently, you save in transaction costs but the P&L volatility will be high. On the other hand, when you hedge frequently, your P&L volatility will be small (still when jumps or stochastic volatility present you cannot hedge all the risk by the delta-hedging) but transaction costs will be prohibitive. The analytical results in the paper help to find the optimal hedging frequency to trade-off between transcation costs and the P&L volatiliy and, as a result, to maximize the Sharpe ratio.If you look at the Figure 7 for the Sharpe ratio under the simple log-normal model, you can see that the range for the Sharpe ratio is from 1.5 to -1.0 as a function of the hedging frequency. There IS a huge difference to the Sharpe ratio coming from the choice of the hedging frequency.
Last edited by
Engy on October 9th, 2015, 10:00 pm, edited 1 time in total.