Sample code to use shiny for multiple graphs in same plot
Use ggplot2 and gridextra
May 4, 2016
Shiny R code for multiple plots using ggplot2 and gridextra
Shiny R code for multiple plots using ggplot2 and gridextra
Sample code to use shiny for multiple graphs in same plot
Use ggplot2 and gridextra
Sample code to use shiny for multiple graphs in same plot
Use ggplot2 and gridextra
Jan 7, 2016
Model free implied volatility
Risk-Neutral Skewness and Kurtosis:
See this post for R code to calculate model free implied volatility.
Let stock price return for period \tau is given by:
\begin{equation} R(t,\tau) \equiv ln[S(t, \tau)]-ln[S(t)] \end{equation}
\begin{equation} H[S]\left\{\begin{matrix} V(t,\tau) \equiv R(t, \tau)^{2} \text{ Volatility contract } & \\W(t,\tau) \equiv R(t, \tau)^{3} \text{ Cubic contract } & \\ X(t,\tau) \equiv R(t, \tau)^{4}\text{ Quadrartic contract } & \end{matrix}\right. \end{equation}
The price of the volatility contract:
\begin{equation} V(t,\tau)=\int_{S(t)}^{\infty }\frac{2(1-ln(K/S(t)))}{K^{2}}C(t,\tau;K)dK+\int_{0}^{S(t)}\frac{2(1-ln(K/S(t)))}{K^{2}}P(t,\tau;K)dK \label{ref1} \end{equation}
The price of the cubic contract:
\begin{equation} W(t,\tau)=\int_{S(t)}^{\infty }\frac{6ln[\frac{K}{S(t)}]-3([\frac{K}{S(t)}])^2}{K^{2}}C(t,\tau;K)dK+\int_{0}^{S(t)}\frac{6ln[\frac{K}{S(t)}]+3([\frac{K}{S(t)}])^2}{K^{2}}P(t,\tau;K)dK \label{ref2} \end{equation}
The price of the quadratic contract:
\begin{equation} X(t,\tau)=\int_{S(t)}^{\infty }\frac{12(ln[\frac{K}{S(t)}])^2-4([\frac{K}{S(t)}])^3}{K^{2}}C(t,\tau;K)dK+\int_{0}^{S(t)}\frac{12(ln[\frac{K}{S(t)}])^2-4([\frac{K}{S(t)}])^3}{K^{2}}P(t,\tau;K)dK \label{ref3} \end{equation}
Define \mu(t, \tau):
\begin{equation} \mu(t,\tau) = e^{r\tau}-1-\frac{e^{r\tau}}{2}V(t,\tau)-\frac{e^{r\tau}}{6}W(t,\tau)-\frac{e^{r\tau}}{24}X(t,\tau) \end{equation}
For \tau-period model-free implied volatility (*MFIV*) is:
\begin{equation} MFIV(t, \tau) = (V(t, \tau))^{1/2} \end{equation}
For \tau-period model free implied skewness(*MFIS*) is:
\begin{equation} MFIS(t, \tau) = \frac{e^{r\tau}W(t,\tau)-3\mu(t,\tau)e^{r\tau}V(t,\tau)+2(\mu(t,\tau))^3}{(e^{r\tau}V(t,\tau)-(\mu(t,tau))^2)^{3/2}} \end{equation}
To calculate the integral in equation (\ref{ref1}), (\ref{ref2}), and (\ref{ref3}), I require continuous option prices from 0 to \infty. For simplicity, I set lower limit and upper limit for integrals.
In the calculation, I use lower limit of strike price K_{L} as the minimum strike price for OTM put option with non zero contract size (or trade quantity).
For upper limit for strike price, K_{U}, I use the maximum strike price of OTM call option with non zero trading size.
References:
Bakshi, G., Kapadia, N., & Madan, D. (2003). Stock return characteristics, skew laws, and the differential pricing of individual equity options. Review of Financial Studies, 16(1), 101-143.
Jiang, George J., and Yisong S. Tian. "The model-free implied volatility and its information content." Review of Financial Studies 18.4 (2005): 1305-1342
See this post for R code to calculate model free implied volatility.
Let stock price return for period \tau is given by:
\begin{equation} R(t,\tau) \equiv ln[S(t, \tau)]-ln[S(t)] \end{equation}
\begin{equation} H[S]\left\{\begin{matrix} V(t,\tau) \equiv R(t, \tau)^{2} \text{ Volatility contract } & \\W(t,\tau) \equiv R(t, \tau)^{3} \text{ Cubic contract } & \\ X(t,\tau) \equiv R(t, \tau)^{4}\text{ Quadrartic contract } & \end{matrix}\right. \end{equation}
The price of the volatility contract:
\begin{equation} V(t,\tau)=\int_{S(t)}^{\infty }\frac{2(1-ln(K/S(t)))}{K^{2}}C(t,\tau;K)dK+\int_{0}^{S(t)}\frac{2(1-ln(K/S(t)))}{K^{2}}P(t,\tau;K)dK \label{ref1} \end{equation}
The price of the cubic contract:
\begin{equation} W(t,\tau)=\int_{S(t)}^{\infty }\frac{6ln[\frac{K}{S(t)}]-3([\frac{K}{S(t)}])^2}{K^{2}}C(t,\tau;K)dK+\int_{0}^{S(t)}\frac{6ln[\frac{K}{S(t)}]+3([\frac{K}{S(t)}])^2}{K^{2}}P(t,\tau;K)dK \label{ref2} \end{equation}
The price of the quadratic contract:
\begin{equation} X(t,\tau)=\int_{S(t)}^{\infty }\frac{12(ln[\frac{K}{S(t)}])^2-4([\frac{K}{S(t)}])^3}{K^{2}}C(t,\tau;K)dK+\int_{0}^{S(t)}\frac{12(ln[\frac{K}{S(t)}])^2-4([\frac{K}{S(t)}])^3}{K^{2}}P(t,\tau;K)dK \label{ref3} \end{equation}
Define \mu(t, \tau):
\begin{equation} \mu(t,\tau) = e^{r\tau}-1-\frac{e^{r\tau}}{2}V(t,\tau)-\frac{e^{r\tau}}{6}W(t,\tau)-\frac{e^{r\tau}}{24}X(t,\tau) \end{equation}
For \tau-period model-free implied volatility (*MFIV*) is:
\begin{equation} MFIV(t, \tau) = (V(t, \tau))^{1/2} \end{equation}
For \tau-period model free implied skewness(*MFIS*) is:
\begin{equation} MFIS(t, \tau) = \frac{e^{r\tau}W(t,\tau)-3\mu(t,\tau)e^{r\tau}V(t,\tau)+2(\mu(t,\tau))^3}{(e^{r\tau}V(t,\tau)-(\mu(t,tau))^2)^{3/2}} \end{equation}
To calculate the integral in equation (\ref{ref1}), (\ref{ref2}), and (\ref{ref3}), I require continuous option prices from 0 to \infty. For simplicity, I set lower limit and upper limit for integrals.
In the calculation, I use lower limit of strike price K_{L} as the minimum strike price for OTM put option with non zero contract size (or trade quantity).
For upper limit for strike price, K_{U}, I use the maximum strike price of OTM call option with non zero trading size.
References:
Bakshi, G., Kapadia, N., & Madan, D. (2003). Stock return characteristics, skew laws, and the differential pricing of individual equity options. Review of Financial Studies, 16(1), 101-143.
Jiang, George J., and Yisong S. Tian. "The model-free implied volatility and its information content." Review of Financial Studies 18.4 (2005): 1305-1342
Jan 1, 2016
Volatility smile
Following code downloads option price data for a day d from NSE website and plot volatility smile :)
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| library(data.table) | |
| library(RQuantLib) | |
| #### For OS x libcurl may not work### | |
| # This code work without quantmode# | |
| NSEIndex = "^NSEI" | |
| # Risk free interest rate fixed at 7.5% | |
| # Source NSE Mibor | |
| riskfree = 0.075 | |
| #Specify date in mm/dd/yyyy | |
| dates = c("01/06/2015") | |
| tdata <- as.Date(dates, format = "%m/%d/%Y") | |
| # Find URL link at NSE website for the bhavcopy of the day | |
| urllink = paste("http://www.nseindia.com/content/historical/DERIVATIVES/",(format(tdata, "%Y")),"/",toupper(format(tdata, "%b")),"/fo",toupper(format(tdata, "%d%b%Y")),"bhav.csv.zip", sep="") | |
| tempzip = paste(toupper(format(tdata, "%d%b%Y")),"bhav.csv.zip", sep="") | |
| tempfilename = paste("fo",toupper(format(tdata, "%d%b%Y")), "bhav.csv", sep="") | |
| # download the compressed file and extract | |
| download.file(urllink,tempzip, mode="wb" , method = "libcurl") | |
| unzip(tempzip, tempfilename, overwrite = T) | |
| optiondf <- read.table(tempfilename, sep=",", header=T) | |
| print("Downloaded derivative market data for the day") | |
| print(head(optiondf)) | |
| # Download or read indices' close price | |
| indexlnk = paste("http://www.nseindia.com/content/indices/ind_close_all_", toupper(format(tdata, "%d%m%Y")),".csv", sep="") | |
| tempindexzip = paste(toupper(format(tdata, "%d%m%Y")),"index.csv", sep="") | |
| download.file(indexlnk,tempindexzip, mode="wb" , method = "libcurl") | |
| indexdf <- read.table(tempindexzip, sep=",", header=T) | |
| print("Downloaded market index data for the day") | |
| print(head(indexdf)) | |
| # get NIFTY 50 Index price | |
| indprice = 0 | |
| # Dataframe for put/call options | |
| optionindxdf = NULL | |
| otmput = NULL | |
| otmcall =NULL | |
| # find NIFTY index price | |
| if(length(indexdf)>0) { | |
| colmhead = "Nifty 50" | |
| if(colmhead %in% indexdf[, 1]){ | |
| indprice = indexdf[indexdf$Index.Name =="Nifty 50","Closing.Index.Value"] | |
| } | |
| else{ | |
| indprice = indexdf[indexdf$Index.Name =="CNX Nifty","Closing.Index.Value"] | |
| } | |
| } | |
| if(length(indexdf)>0) { | |
| # Near expirty date | |
| optiondfEDT = as.Date(optiondfEXPIRY_DT, "%d-%b-%Y") | |
| # Days to maturity | |
| optiondfdtm = as.numeric(optiondfEDT - tdata) | |
| nearexp = min(optiondf[(optiondfdtm>20) & (optiondfdtm<100), "EDT"]) | |
| optselindx = (optiondfINSTRUMENT=="OPTIDX") & (optiondfSYMBOL=="NIFTY") & (optiondfCONTRACTS>0) & (optiondfEDT==nearexp) | |
| optionindxdf = data.table(optiondf[optselindx, ]) | |
| # Out of money call and put options | |
| otmput = optionindxdf[(optionindxdfOPTION_TYP=="PE") & (optionindxdfSTRIKE_PR<indprice), ][order(STRIKE_PR)] | |
| otmcall = optionindxdf[(optionindxdfOPTION_TYP=="CE") & (optionindxdfSTRIKE_PR>indprice), ][order(STRIKE_PR)] | |
| otmput$X = NULL | |
| otmcall$X = NULL | |
| print("Call option details:") | |
| print(head(otmcall)) | |
| print("Put option details:") | |
| print(head(otmput)) | |
| # Calculate implied volatility | |
| idx = seq(1, dim(otmput)[1]) | |
| otmput$IV = 0.01 | |
| for(j in idx){ | |
| oval = otmput[j, CLOSE] | |
| stk = otmput[j, STRIKE_PR] | |
| # Annualized days | |
| matrty = otmput[j, dtm]/360.0 | |
| dvdyld = 0 | |
| expvol = 0.1 | |
| civ = EuropeanOptionImpliedVolatility(type="put", value=oval, underlying=indprice, strike=stk, dividendYield=dvdyld, riskFreeRate=riskfree, maturity=matrty, volatility=expvol) | |
| otmput$IV[j] = civ | |
| } | |
| idx = seq(1, dim(otmcall)[1]) | |
| otmcall$IV = 0.01 | |
| for(j in idx){ | |
| oval = otmcall[j, CLOSE] | |
| stk = otmcall[j, STRIKE_PR] | |
| matrty = otmcall[j, dtm]/360.0 | |
| dvdyld = 0 | |
| expvol = 0. | |
| civ = EuropeanOptionImpliedVolatility(type="call", value=oval, underlying=indprice, strike=stk, dividendYield=dvdyld, riskFreeRate=riskfree, maturity=matrty, volatility=expvol) | |
| otmcall$IV[j] = civ | |
| } | |
| # Plot the volatility smile/smirk | |
| smirkval = c(otmputIV, otmcallIV) | |
| smirkstk = c(otmputSTRIKE_PR, otmcallSTRIKE_PR) | |
| plot(smirkstk, smirkval, xlab="Strike", ylab= "Implied volatility", main ="Volatility smile", type="l", col = "dark red") | |
| abline(v=indprice, col="blue") | |
| text(indprice, 0.2, "Stock Price") | |
| } | |
Dec 31, 2015
R code to download Options and Futures data from NSE
The code below can download daily bhav for Futures and Options from the NSE website.
I have also include sample code that downloads indices level from the National Stock Exchange
I have also include sample code that downloads indices level from the National Stock Exchange
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| #### For OS x libcurl may not work### | |
| # This code work without quantmode# | |
| NSEIndex = "^NSEI" | |
| # Risk free interest rate fixed at 7.5% | |
| # Source NSE Mibor | |
| riskfree = 0.075 | |
| #Specify date | |
| dates = c("12/28/2015") | |
| tdata <- as.Date(dates, format = "%m/%d/%Y") | |
| # Find URL link at NSE website for the bhavcopy of the day | |
| urllink = paste("http://www.nseindia.com/content/historical/DERIVATIVES/",(format(tdata, "%Y")),"/",toupper(format(tdata, "%b")),"/fo",toupper(format(tdata, "%d%b%Y")),"bhav.csv.zip", sep="") | |
| tempzip = paste(toupper(format(tdata, "%d%b%Y")),"bhav.csv.zip", sep="") | |
| tempfilename = paste("fo",toupper(format(tdata, "%d%b%Y")), "bhav.csv", sep="") | |
| # download the compressed file and extract | |
| download.file(urllink,tempzip, mode="wb" , method = "libcurl") | |
| unzip(tempzip, tempfilename, overwrite = T) | |
| optiondf <- read.table(tempfilename, sep=",", header=T) | |
| print("Downloaded derivative market data for the day") | |
| print(head(optiondf)) | |
| # Download or read indices' close price | |
| indexlnk = paste("http://www.nseindia.com/content/indices/ind_close_all_", toupper(format(tdata, "%d%m%Y")),".csv", sep="") | |
| tempindexzip = paste(toupper(format(tdata, "%d%m%Y")),"index.csv", sep="") | |
| download.file(indexlnk,tempindexzip, mode="wb" , method = "libcurl") | |
| indexdf <- read.table(tempindexzip, sep=",", header=T) | |
| print("Downloaded market index data for the day") | |
| print(head(indexdf)) |
Sep 3, 2015
Factor to explain factor
The new fama-french model replaces the existing five-factor model. The new five-factor fama-french model includes profitability and investment factors.
Profitability factor: Robust minus weak operating profit (RWA )= (SR + BR) / 2 – (SW + BW) / 2 = [(SR – SW) + ( BR - BW)] / 2
Investment factor: Conservative minus aggressive Investment (CMA) = (SC + BC) / 2 – (SA + BA) / 2 = [(SC – SA) + ( BC -BA)] / 2
Investment factor: Conservative minus aggressive Investment (CMA) = (SC + BC) / 2 – (SA + BA) / 2 = [(SC – SA) + ( BC -BA)] / 2
S = small ; B = big; R = Robust; W= Weak; C= Conservative; A = Aggressive
The new model is:
R_{t}-RF_{t} = \alpha + \beta_{1}[RM_{t}-RF_{t}] + \beta_{2}SMB_{t} + \beta_{3}HML_{t} + \beta_{4}RMW_{t} + \beta_{5}CMA_{t} + \epsilon_{t}
RM_{t}-RF_{t} = excess market return
SMB_{t} = the Size factor
HML_{t} = the value factor
RMW_{t} = the profitability factor
CMA_{t} = the investment factor
RF_{t} = risk free rate
The new model is:
R_{t}-RF_{t} = \alpha + \beta_{1}[RM_{t}-RF_{t}] + \beta_{2}SMB_{t} + \beta_{3}HML_{t} + \beta_{4}RMW_{t} + \beta_{5}CMA_{t} + \epsilon_{t}
RM_{t}-RF_{t} = excess market return
SMB_{t} = the Size factor
HML_{t} = the value factor
RMW_{t} = the profitability factor
CMA_{t} = the investment factor
RF_{t} = risk free rate
Jun 27, 2013
Good resources for research papers
General Working Papers:
EconPapers: Very large collection of economics working papers
Look at Repec too
University wise working paper series:
Harvard Working Paper 1
Harvard Business School Working Paper Archive
London Business School Working Papers
Sloan School of Management Working Papers Index
University of Chicago Center for Research in Security Prices (CRSP)
University of Michigan Business School
Yale School of Management
Look at Repec too
University wise working paper series:
Harvard Working Paper 1
Harvard Business School Working Paper Archive
London Business School Working Papers
Sloan School of Management Working Papers Index
University of Chicago Center for Research in Security Prices (CRSP)
University of Michigan Business School
Yale School of Management
International Organizations:
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