# Quantitative Finance Collector is a blog on Quantitative finance analysis, financial engineering methods in mathematical finance focusing on derivative pricing, quantitative trading and quantitative risk management. Random thoughts on financial markets and personal staff are posted at the sub personal blog.

Nov
13

I have written a working paper on CDS (credit default swap) implied stock volatility and found some interesting results. Post it here just in case someone is interested.

Both CDS and out-of-money put option can protect investors against downside risk, so they are related while not being mutually replaceable. This study provides a straightforward linkage between corporate CDS and equity option by inferring stock volatility from CDS spread and, thus, enables a direct analogy with the implied volatility from option price. I find CDS inferred volatility (CIV) and option implied volatility (OIV) are complementary, both containing some information that is not captured by the other. CIV dominates OIV in forecasting stock future realized volatility. Moreover, a trading strategy based on the CIV-OIV mean reverting spreads generates significant risk-adjusted return. These findings complement existing empirical evidence on cross-market analysis.

Mar
12

Journal of Econometrics accepts several papers on option pricing, some are quite interesting and represent the recent developments of this field. I list them here just in case you are also interested.

http://www.sciencedirect.com/science/article/pii/S0304407615000615

http://www.sciencedirect.com/science/article/pii/S0304407615000585

**Smile from the Past: A general option pricing framework with multiple volatility and leverage components**In the current literature, the analytical tractability of discrete time option pricing models is guaranteed only for rather specific types of models and pricing kernels. We propose a very general and fully analytical option pricing framework, encompassing a wide class of discrete time models featuring multiple-component structure in both volatility and leverage, and a flexible pricing kernel with multiple risk premia. Although the proposed framework is general enough to include either GARCH-type volatility, Realized Volatility or a combination of the two, in this paper we focus on realized volatility option pricing models by extending the Heterogeneous Autoregressive Gamma (HARG) model of Corsi et al. (2012) to incorporate heterogeneous leverage structures with multiple components, while preserving closed-form solutions for option prices. Applying our analytically tractable asymmetric HARG model to a large sample of S&P 500 index options, we demonstrate its superior ability to price out-of-the-money options compared to existing benchmarks.

http://www.sciencedirect.com/science/article/pii/S0304407615000615

**Option pricing with non-Gaussian scaling and infinite-state switching volatility**Volatility clustering, long-range dependence, and non-Gaussian scaling are stylized facts of financial assets dynamics. They are ignored in the Black & Scholes framework, but have a relevant impact on the pricing of options written on financial assets. Using a recent model for market dynamics which adequately captures the above stylized facts, we derive closed form equations for option pricing, obtaining the Black & Scholes as a special case. By applying our pricing equations to a major equity index option dataset, we show that inclusion of stylized features in financial modeling moves derivative prices about 30% closer to the market values without the need of calibrating models parameters on available derivative prices.

http://www.sciencedirect.com/science/article/pii/S0304407615000585

Oct
27

I have co-authored a short paper with a friend in Zhejiang University, forthcoming in the Finance Research Letters, titled "Sell in May and Go Away: Evidence from China".

As the abstract suggests, basically we aim to examine whether the sell-in-may phenomenon existed in developed country also happens in China, and if Yes, if there is any special reason to explain it, which has implications for those international investors as MSCI plans to add Chinese A shares to its emerging index from May 2015, and as the recent China's stock market plan that permits Hong Kong investors to trade designated stocks in Shanghai Exchange market directly. People would expect investing in China provides a diversified strategy.

Using the Chinese stock market data from 1997 to 2013, this paper examines the “Sell in May and Go Away” puzzle first identified by Bouman and Jacobsen (2002). We find strong existence of the Sell in May effect, robust to different regression assumptions, industries, and after controlling for the January or February effect. However, part of the puzzle is subsumed by the seasonal affective disorder effect. We then construct a trading strategy based on this puzzle, and find that it outperforms the buy-and-hold strategy and could resist the market downside risk during large recession periods.

As the abstract suggests, basically we aim to examine whether the sell-in-may phenomenon existed in developed country also happens in China, and if Yes, if there is any special reason to explain it, which has implications for those international investors as MSCI plans to add Chinese A shares to its emerging index from May 2015, and as the recent China's stock market plan that permits Hong Kong investors to trade designated stocks in Shanghai Exchange market directly. People would expect investing in China provides a diversified strategy.

Mar
10

Han, Y.F., and Zhou, G.F. have an interesting working paper on the performance of a trend factor they proposed:

The basic idea is to first calculate the month-end price moving average time series of different lags, then regress cross-sectionally monthly returns at date t on all moving average series at date t-1, finally predict monthly returns at date t+1 using the regression estimates and the moving average series at date t. This procedure guarantees we forecast stock returns at t+1 with information set only up to t. We then rank all stocks based on the forecasts into five quintiles, long the quintile with highest forecast returns and short the quintile with lowest, and rebalance once per month. This strategy generates, on average, 1.61% monthly return and 0.29 sharpe ratio using all US stocks, performs especially good during recession, and outperforms several existing factors. Moreover, the good performance of this strategy cannot be explained by firm fundamentals.

I implement this strategy with Chinese stock data, adjust the rebalance frequency to weekly for convenience, and trade in extreme by always long the one stock with the highest forecast return, no short is allowed, stop loss is set at 5%. The result is amazing, it yields an annualized return at 97.15% from March, 2013 to Feb, 2014, with maximum drawdown at 30.01%. The fund curve is as follows (note: I didn't use all Chinese stocks but only 840 stocks in my stock pool with good liquidity, so there is selection bias and please accept the result cautiously...)

Nice shot. It seems to be better than the simple strategy between A-shares and H-shares.

In this paper, we propose a trend factor to capture cross-section stock price trends. In contrast to the popular momentum factor constructed by sorting stocks based on a single criterion of past year performance, we form our trend factor with a cross-section regression approach that makes use of multiple trend indicators containing daily, weekly, monthly and yearly information. We find that the average return on the trend factor is 1.61% per month, more than twice of the momentum factor. The Sharpe ratio is more than twice too. Moreover, during the recent financial crisis, the trend factor earns 1.65% per month while the momentum factor loses 1.33% per month. The trend factor return is robust to a variety of control variables including size, prior month return, book-to-market, idiosyncratic volatility, liquidity, etc., and is greater under greater information uncertainty. In addition, the trend factor explains well the cross-section decile portfolio returns sorted by short-term reversal, momentum, and long-term reversal as well as various price ratios (e.g. E/P), and performs much better than the momentum factor.

The basic idea is to first calculate the month-end price moving average time series of different lags, then regress cross-sectionally monthly returns at date t on all moving average series at date t-1, finally predict monthly returns at date t+1 using the regression estimates and the moving average series at date t. This procedure guarantees we forecast stock returns at t+1 with information set only up to t. We then rank all stocks based on the forecasts into five quintiles, long the quintile with highest forecast returns and short the quintile with lowest, and rebalance once per month. This strategy generates, on average, 1.61% monthly return and 0.29 sharpe ratio using all US stocks, performs especially good during recession, and outperforms several existing factors. Moreover, the good performance of this strategy cannot be explained by firm fundamentals.

I implement this strategy with Chinese stock data, adjust the rebalance frequency to weekly for convenience, and trade in extreme by always long the one stock with the highest forecast return, no short is allowed, stop loss is set at 5%. The result is amazing, it yields an annualized return at 97.15% from March, 2013 to Feb, 2014, with maximum drawdown at 30.01%. The fund curve is as follows (note: I didn't use all Chinese stocks but only 840 stocks in my stock pool with good liquidity, so there is selection bias and please accept the result cautiously...)

Nice shot. It seems to be better than the simple strategy between A-shares and H-shares.

Feb
3

*A similar article was posted at the sub-personal blog before and I paste it here in case someone is interested.*

At the moment there are 84 firms listed at both A (Shanghai and Shenzhen) and H (Hongkong) stock markets, according to the law of one price, the stock prices of these firms should be at similar level. However, there are huge differences, without considering exchange rate (1 RMB = 1.28 HK$), the ratio of the price in A market to the price in H market for a same firm is as low as 52.72% and as high as 617.59% as of 02/03/2014. Is the difference mean reverting? If yes, we would expect the stock traded cheaper in A market to go up, and vice versa. So can we make profit by long the stocks with large differences?

Rigorous statistical method should be undertaken to examine whether the ratio is indeed mean reverting. For simplicity, I construct a trading strategy that each week, I go long at the opening price the stock in A market that has the smallest price ratio of previous week, hold it one week and sell it at the weekly closing price. Short trading is not allowed for individual investor in A market. Stop loss is set arbitrarily at 5%. Transaction cost is 0.18% per trading.

The results for this simple strategy from 02.2013 to 01.2014 are:

Annualized Return 0.2070

Annualized Std Dev 0.2545

Annualized Sharpe 0.8133

Maximum Drawdown

From Trough To Depth Length To Trough Recovery

1 2013-09-13 2013-12-13 -0.1275 19 12 NA

2 2013-08-16 2013-08-23 2013-09-06 -0.0566 4 2 2

3 2013-03-22 2013-04-19 2013-05-03 -0.0488 5 3 2

4 2013-07-12 2013-07-12 2013-07-19 -0.0374 2 1 1

5 2013-05-31 2013-05-31 2013-07-05 -0.0229 6 1 5

The fund curve

Lower line is the return for a buy-and-hold strategy of all 84 firms.

Considering the fact that 2013 is a gloomy year for A market and this strategy is long only, the performance is not bad at all. Comments are welcomed