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I want to model energy prices. I have two markets, lets say market 1 and 2.
Market 1 is continuously traded, and I will assume it follows brownian motion. So the value of the asset could be defined like this on this market alone.
$$dS = \mu dt + \sigma dW$$
with $dW = \epsilon \sqrt{dt}$ and $\epsilon \sim \ma... |
The shape of the volatility curve in index options trading typically shows that the 'just' ITM Calls (OTM Puts) options have the lowest implied volatility.
If you are long an ATM Call and the market moves down I see two results;
1. That Call should now be approaching the bottom of the curve and its implied volati... |
Maturity is the "cousin" of volatility, it is almost everything. Other item to think about include is it an American or European exercise? But its all about volatility and time, all else being equal. |
I want to model energy prices. I have two markets, lets say market 1 and 2.
Market 1 is continuously traded, and I will assume it follows brownian motion. So the value of the asset could be defined like this on this market alone.
$$dS = \mu S dt + \sigma S dW$$
with $dW = \epsilon \sqrt{dt}$ and $\epsilon \sim... |
I am reading SOFR USER Guide - https://www.newyorkfed.org/medialibrary/Microsites/arrc/files/2019/Users_Guide_to_SOFR.pdf
I am having trouble understanding SOFR payment in arrears, especially lockout and lookback.
**Lockout or Suspension Period**: Use the averaged SOFR over current interest period with last rat... |
I am reading SOFR USER Guide - https://www.newyorkfed.org/medialibrary/Microsites/arrc/files/2019/Users_Guide_to_SOFR.pdf
I am having trouble understanding SOFR payment in arrears, especially lockout and lookback.
**Lockout or Suspension Period**: Use the averaged SOFR over current interest period with last rat... |
I have been looking at the following post (and comparing it to SWPM in Bloomberg)
https://kiandlee.blogspot.com/2021/07/interest-rate-swap-pricing-using-r.html
Why does the fixed leg accrue in 30/360 yet the floating leg accrues actual/365?
Is there some logic behind this? |
Why is the fixed leg of a libor swap 30/360 and the floating is actual/360? |
I know this answer is years later but in case anyone looks this up, I'm hoping I can help.
I can go through all of the mathematical proofs, but instead I'll try to give some intuition.
By way of background, functions that are non-differentiable at any point but continuous at every point was first discovered by... |
We can solve the Black Scholes PDE by numerical methods like Euler
\begin{equation}
\frac{\partial V}{\partial t} + rS\frac{\partial V}{\partial S}+\frac{1}{2} \sigma^2 S^2\frac{\partial^2 V}{\partial S^2}-rV=0
\end{equation}
In order to do that, we need to discretize the stock space. A simple way is to set a range... |
Assume a sufficiently 'wide and dense' mesh of sampling points $(S_i,t_j), i=0..N, j=0..M$, $S_i=S_{low}+i\Delta S$, $t_j=j\Delta t$. Given the payoff encoded in $v_{i,M}$ and some boundary conditions for $j=M$, sarting from $j=M$ backwards, an explicit recursive numerical approximation scheme to the value equation the... |
Assume a sufficiently 'wide and dense' mesh of sampling points $(S_i,t_j), i=0..N, j=0..M$, $S_i=S_{low}+i\Delta S$, $t_j=j\Delta t$. Given the payoff encoded in $v_{i,M}$ and some boundary conditions for $j=M$, sarting from $j=M$ backwards, an explicit recursive numerical approximation scheme to the value equation the... |
Assume a sufficiently 'wide and dense' mesh of sampling points $(S_i,t_j), i=0..N, j=0..M$, $S_i=S_{low}+i\Delta S$, $t_j=j\Delta t$. Given the payoff encoded in $v_{i,M}$ and some boundary conditions for $j=M$, sarting from $j=M$ backwards, an explicit recursive numerical approximation scheme to the value equation the... |
The shape of the volatility curve in index options trading typically shows that the 'just' OTM Calls (ITM Puts) options have the lowest implied volatility.
If you are long an ATM Call and the market moves down I see two results;
1. That Call should now be approaching the bottom of the curve and its implied volati... |
I was reading "We Don’t Quite Know What We Are Talking About When We Talk About Volatility" by Goldstein and Taleb, and I was trying to quickly verify numerically the relation between mean deviation and standard deviation.
However, I get that 0.8 is the ratio between **mean deviation and variance**, not **mean devia... |
A concept of accumulation and distribution process was developed by Richard Wyckoff. In simple words a smart money sells shares in order to hit its buy limit orders, then starts to buy shares in order to hit its sell limit order. But here are the questions:
>1.Who is such smart money? A market maker or some insider?
... |
I am working with a team on a market making algorithm on Huobi. We are integrating our infrastructure in AWS and when you are a S tier you can get a privatelink which is about 10 to 50 ms faster than routing thru public networks. Are there any serious market makers here who have experienced the difference? It may be a ... |
Except for the fact that in equilibrium demand must equal supply, I do not understand why, by chance, this tangency portfolio is the market portfolio. Do you have any idea? |
Why is the tangency portfolio the market portfolio? |
Let us consider a stochastic market model with a fixed short (risk-free) rate $r\in\mathbb{R}$. A trader can obtain unsecured funding at a rate $f_t:=r+s_t$ where $s_t$ is its stochastic funding spread. We assume this spread follows geometric Brownian Motion dynamics:
$$\label{model:fnd-sprd}\tag{1}
\text{d}s_t=\sigma ... |
It is not simply supply and demand. There was supply and demand for options before October 1987, yet, options traded largely without a skew. Supply and demand plays a role, but its a secondary consideration.
Implied vol is a way of turning an option price into a comparable number (its annualized for example). The t... |
Let us consider a stochastic market model with a fixed short (risk-free) rate $r\in\mathbb{R}$. A trader can obtain unsecured funding at a rate $f_t:=r+s_t$ where $s_t$ is its stochastic funding spread. We assume this spread follows geometric Brownian Motion dynamics:
$$\label{model:fnd-sprd}\tag{1}
\text{d}s_t=\sigma ... |
Let us consider a stochastic market model with a fixed short (risk-free) rate $r\in\mathbb{R}$. A trader can obtain unsecured funding at a rate $f_t:=r+s_t$ where $s_t$ is its stochastic funding spread. We assume this spread follows geometric Brownian Motion dynamics:
$$\label{model:fnd-sprd}\tag{1}
\text{d}s_t=\sigma ... |
how would one formally calculate the portfolio weight of a Forward position?
Suppose I have 100 mio portfolio. I have 50mio in Tesla shares and I have 50mio in Microsoft shares, and I enter into a 1 year forward contract with notional 50mio to receive Apple shares at a price of K. (such that at inception the forward... |
How do trading platforms estimate options pricing P&L graphs? |
Assume a financial instrument which has a (roughly) log-normal price distribution and behaves like a random walk. I would like to generate some possible scenarios for where the price might be tomorrow.
Knowing that the prices are log-normally distributed (and hence skewed, i.e. an increase in price is usually greate... |
Should future price scenarios be symmetric around the current market price? |
I scoured this forum, looking for some indicative (updated as of year 2021) comparison of volatility/option-pricing models. There were some, but they seem dispersed and lacking in general details...
Are there any good papers/forums where there is a good summary? Not looking for anything exhaustive, but along the lines... |
Can anyone help me in understanding how we get the line I have marked with a red arrow?
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/rhdQI.png
I guess I have trouble in understanding the difference between differentials and derivatives, i.e. what is the difference between e.g., $d... |
I am working on a SABR-LMM model with the following system of SDEs under a numeraire $N$:
$$
\begin{align}
&\mathrm{d} F_i(t) = \sigma_i (t) (F_i(t) + s)^{\beta} \Big( \mu^f_i (t) \mathrm{d}t + \mathrm{d} W^{N}_i(t) \Big) \ , \notag \\
&\mathrm{d} \sigma_i(t) = \nu_i \sigma_i(t) \Big( \mu^\sigma_i (t) \... |
How can I reproduce the implied volatility curve (plotted against the strike price) in the Heston model (i.e. the blue line in the graph below)?
>What's the equation that I have to set up and solve?
I have a function the evaluates the price of a Heston call:
heston_call$(S_0, v_0, \theta, \kappa, \eta, r, \rh... |
How can I reproduce the implied volatility curve (plotted against the strike price) in the Heston model (i.e. the blue line in the graph below)?
>What's the equation that I have to set up and solve?
I have a function that evaluates the price of a Heston call:
heston_call$(S_0, v_0, \theta, \kappa, \eta, r, \r... |
How can I reproduce the implied volatility curve (plotted against the strike price) in the Heston model (i.e. the blue line in the graph below)?
>What's the equation that I have to set up and solve?
I have a function that evaluates the price of a Heston call:
heston_call$(S_0, v_0, \theta, \kappa, \eta, r, \r... |
Do different debt tiers have different probability of default?
Many thanks!! |
Given 10 years history of past balances of deposit accounts in a commercial bank, I need to calculate what part of those deposits were core, month by month.
This is my thinking: for each account/month take the minimum balance of that month. Then add up all the minimum balances for the month, and that will be the ban... |
I would like to ask if different debt seniorities ( like senior unsecured bonds and subordinated bonds) have different probability of default?
(Before edited I used debt tiers instead of seniority but I guess that is not the correct terminology)
For example, my initial understanding was that different debt tiers ... |
I was thinking about cointegrated time series and came up with the following simultaneous equations model:
$dY_t = \alpha (Y_t - \gamma X_t)dt + \sigma dB_t$
$dX_t = \beta (Y_t - \delta X_t)dt + \tau dW_t$
$dW_t dB_t = \rho dt$
With greek letters constants.
Is it possible to find analytical solutions for... |
I was thinking about cointegrated time series and came up with the following simultaneous equations model:
$dY_t = \alpha (Y_t - \gamma X_t)dt + \sigma dB_t$
$dX_t = \beta (Y_t - \delta X_t)dt + \tau dW_t$
$dW_t dB_t = \rho dt$
With greek letters constants. $\alpha$ and $\beta$ with opposite signs.
Is it... |
I am trying to use in a trading strategy the STC indicator, but I can not find out why its not working properly.
The chart that I am using is BTC/USDT on UTC as a timeframe.
Chart time: ***01 Feb 22 - 16:20 UTC***
------------------- TradingView: ------------------------
**STC value: 97.66**
**STC settin... |
I'm trying to understand whether notional resets on a floating-floating cross-currency basis swap play a role or not when the coupon payments are SOFR-based (with no spread) and they are discounted with the same SOFR rate.
From section 6.5.2.3 in Andersen-Piterbarg, we have
$$\begin{align*}
V_\text{basisswap,\$... |
I have the following SDE
\begin{equation}
dX_t = - \frac{1}{1+t}X_t dt + \frac{1}{1+t}dB_t
\end{equation}
that has the solution:
\begin{equation}
\begin{aligned}
X_t = \frac{X_0 + B_t}{1+t} = \frac{B_t}{1+t} \;\;\; X_0 = 0
\end{aligned}
\end{equation}
Now how can I show that this is a strong solution?... |
I have a MC simulation that uses finite differences to calculate the Greeks. It's for baskets and calendar spreads mostly.
Now the logical (to me anyway) approach to calculate Vega is to increase the input volatility by 1% (annual vol) for each leg (leg1 Vega: leg1 vol + 1%, leg2 Vega: leg2 vol + 1%, etc.), reprice... |
I'm trying to understand whether notional resets on a floating-floating cross-currency basis swap play a role or not when the coupon payments are SOFR-based (with no spread) and they are discounted with the same SOFR rate.
From section 6.5.2.3 in Andersen-Piterbarg, we have
$$
\begin{align}
V_\text{basisswap,\... |
I am trying to use in a trading strategy the STC indicator, but I can not find out why its not working properly.
The chart that I am using is BTC/USDT on UTC as a timeframe.
Chart time: ***01 Feb 22 - 16:20 UTC***
------------------- TradingView: ------------------------
**STC value: 97.66**
**STC settin... |
I'm trying to understand whether notional resets on a floating-floating cross-currency basis swap play a role or not when the coupon payments are SOFR-based (with no spread) and they are discounted with the same SOFR rate.
From section 6.5.2.3 in Andersen-Piterbarg, we have
\begin{align}
V_\text{basisswap,\$}(0... |
I'm trying to understand whether notional resets on a floating-floating cross-currency basis swap play a role or not when the coupon payments are SOFR-based (with no spread) and they are discounted with the same SOFR rate.
From section 6.5.2.3 in Andersen-Piterbarg, we have
\begin{align*}
V_\text{basisswap,\$}(0)... |
How can I reproduce the implied volatility curve (plotted against the strike price) in the Heston model (i.e. the blue line in the graph below)?
>What's the equation that I have to set up and solve?
I have a function that evaluates the price of a Heston call:
heston_call$(S_0, v_0, \theta, \kappa, \eta, r, \r... |
How can I reproduce the implied volatility curve (plotted against the strike price) in the Heston model (i.e. the blue line in the graph below)?
>What's the equation that I have to set up and solve?
I have a function that evaluates the price of a Heston call:
heston_call$(S_0, v_0, \theta, \kappa, \eta, r, \r... |
Answering versus your specific queries
- Against which analytical formula or numerical method can I compare my simulation results?
Basic would be to benchmark the accuracy against European Swaptions as priced ATM,and ITM/OTM versus the SABR-zero-shift model. Ths is fundamental to make sure the LMM can properly r... |
Did you try using your tool for vanilla options (a single underlying)? Technically, Black Scholes Greeks are for infinitesimally small changes (not 1%).
That said, making shifts too small is dangerous - especially with numerical methods because you can get into an area where your standard error will be bigger than t... |
They only display a chart? No values? What is the platform?
If that is just a plot, I am inclined to say all they do is to run Black Scholes, shorten the time (if you go 6m into the future, just make the expiry 6m shorter), and reprice with a few different spot values. I don't think there is anything fancy. If it's... |
They only display a chart? No values? What is the platform?
If that is just a plot, I am inclined to say all they do is to run Black Scholes, shorten the time (if you go 6m into the future, just make the expiry 6m shorter), and reprice with a few different spot values. I don't think there is anything fancy. If it's... |
I understand that Exchange Traded Interest Options (USD Libor 3m or Euribor 3m) trade with a lower volatility than the respective Cap or Floor for an equivalent structure.
Can anyone give any colour as to the specific reasons for this? Liquidity / One-Way demand in OTC? And are there any research / papers on this... |
I'm working on an academic project that requires data for options tracking ~300 large Japanese stocks between 2010$-$2020.
The standard data source I've seen quoted in academic papers is OptionMetrics, but my academic institution only has a subscription to US markets.
**What are some data sources that give Japa... |
New to the quant finance exchange. I am stuck with a question maybe someone could help me.
In the table below I have calculated if price is up/down w.r.t to the open shown in the 2nd column with pluses and minuses. I have done this for today and then concatenated yesterdays price changes with today in the second r... |
[![enter image description here][1]][1]
This is throwing me for a loop. in regards to this passage, does the M^L represent to perform this sum over every "overlapping window" individually? Would this mean "M symbols" are the unique symbols to that specific window?
[1]: https://i.stack.imgur.com/48Ult.png |
What does M^L represent over this Sigma? |
I was asked to show that the price of a digital/binary option $D$ while a volatility smile $\sigma(K)$ is present is given by
> $$D= \exp(-rT)[ \Phi(d_2) - K \sqrt{T} \phi(d_2) \sigma ' (K)]$$
Where $\Phi$ is the standard normal CDF and $\phi$ is the standard normal pdf.
I started with showing that the price of... |
I was asked to show that the price of a digital/binary option $D$ while a volatility smile $\sigma(K)$ is present is given by
> $$D= \exp(-rT)( \Phi(d_2) - K \sqrt{T} \phi(d_2) \sigma ' (K))$$
Where $\Phi$ is the standard normal CDF and $\phi$ is the standard normal pdf.
I started with showing that the price of... |
As a part of my self learning process, I'm trying to gather the list of volatility indices for all major asset classes.
Equity: CBOE VIX (US), VSTOXX (EU), ?? (UK), ?? (JPY)
Commodities: BCOM (Bloomberg Commodity Vol Index)
Interest Rates: ??
Credit: ??
Real Estate: ??
Cash: ??
What are the prefer... |
What are the volatility Indices for different asset classes? Particularly fixed income & RE? |
As a part of my self learning process, I'm trying to gather the list of volatility indices for all major asset classes.
Equity: CBOE VIX (US), VSTOXX (EU), ?? (UK), ?? (JPY)
Commodities: BCOM (Bloomberg Commodity Vol Index)
Interest Rates: ??
Credit: ??
FX: ??
Real Estate: ??
Cash: ??
What are ... |
As a part of my self learning process, I'm trying to gather the list of volatility indices for all major asset classes.
Equity: CBOE VIX (US), VSTOXX (EU), ?? (UK), ?? (JPY)
Commodities: ??
Interest Rates: ??
Credit: ??
FX: ??
Real Estate: ??
Cash: ??
What are the preferred Volatility indices f... |
As a part of my self learning process, I'm trying to gather the list of volatility indices for all major asset classes.
Equity: CBOE VIX (US), VSTOXX (EU), ?? (UK), ?? (JPY)
Commodities: ??
Interest Rates: ??
Credit: ??
FX: ??
Real Estate: ??
Cash: ??
What are the preferred Volatility indices f... |
As a part of my self learning process, I'm trying to gather the list of volatility indices for all major asset classes.
Equity: CBOE VIX (US), VSTOXX (EU), ?? (UK), ?? (JPY)
Commodities: ??
Interest Rates: MOVE index, SRVIX, ??
Credit: ??
FX: ??
Real Estate: ??
Cash: ??
What are the preferred V... |
Let's say that we have the variance of the daily return at $t_0$:
$$\sigma_{r_{t_0}}^2=\text{Var}[r_{t_0}]=\text{Var}[\frac{S_{t_0}-S_{t_0-1}}{S_{t_0-1}}]$$
for price process $S_t$. Is there a way to derive the formula for variance of the price at moment $t_0$ ($\text{Var}[S_{t_0}]$)? I tried thinking of $S_{t_0-1}$ ... |
As a part of my self learning process, I'm trying to gather the list of volatility indices for all major asset classes.
Equity: CBOE VIX (US), VSTOXX (EU), ?? (UK), ?? (JPY)
Commodities: ??
Interest Rates: MOVE index, SRVIX, ??
Credit: ??
FX: DBCVIX, ??
Real Estate: ??
Cash: ??
What are the pre... |
I am reading material reference rates calculation for SONIA by refinitiv. It says the data is calculated based on OIS Rates between 10:50AM and 11:00 AM.
https://www.refinitiv.com/content/dam/marketing/en_us/documents/methodology/refinitiv-term-sonia-benchmark-statement.pdf
I have following questions:
1. Wh... |
Let's say that we have the variance of the daily return at $t_0$:
$$\sigma_{r_{t_0}}^2=\text{Var}[r_{t_0}]=\text{Var}[\frac{S_{t_0}-S_{t_0-1}}{S_{t_0-1}}]$$
for price process $S_t$. Is there a way to derive the formula for variance of the price at moment $t_0$ ($\text{Var}[S_{t_0}]$)? I tried thinking of $S_{t_0-1}$ ... |
I think it's best to start with explaining what the VIX actually is, because I think afterwards it will be clear(er) why indices like that don't exist for everything you ask for (or are not usually used).
The VIX index is theoretically the square root of the variance swap strike and computed via SPX options that ar... |
Suppose that an Asian option is quoted OTC in terms of its implied volatility. What is the meaning of an implied volatility in this case? Is it an implied volatility of a vanilla European option with the same price, strike and maturity? |
What is the meaning of an implied volatility of an Asian option? |
I would like to calculate the term structure of the VVIX index.
Only way I have found so far is forecasting historical prices N months out.
Any other idea? |
No, you cannot reverse engineer the variance of the prices from the variance of the returns because the variance of the returns must be infinite for any credible candidate distribution for prices. That does not imply that you cannot get information about the variance of prices, but not from the variance of returns.
... |
I think it's best to start with explaining what the VIX actually is, because I think afterwards it will be clear(er) why indices like that don't exist for everything you ask for (or are not usually used).
The VIX index is theoretically the square root of the variance swap strike and computed via SPX options that ar... |
I have the following optimisation problem which I want to solve using linear optimisation.
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/hlUZp.png
Is there a way to represent the second constraint in a linear form in order to be able to use linear optimisation ?
|
Currently bonds are widening almost across all maturities and sectors.
I'm looking at some senior bonds with maturities of less than 1 year, that have widened more than 100bps. This happened even though there is a pull to par on the bonds.
How can I calculate the pull to par effect?
Thank you |
How do you calculate pull to par effect on z-spread? |
I was given the task to decide whether it is a good time to invest into a certain stock index (e.g. S&P 500) or not given a 6 months Investment horizon. The goal is to get one of the following answers: "invest" or "don't invest"
Explanatory variables should be macroeconomic ones such as VIX, EURUSD,10y Treasury yiel... |
I am trying to create a zero curve from a series of government bonds by minimizing the differences in the dirty prices.
The problem is that there is something wrong with my differential evolution algorithm.
My process is as follows:
1. I have utilized quantlib to generate the cash flow schedules and year fra... |
I assume you are talking about credit spreads ( ie the difference in yield between your bond and some risk free reference bond of the same maturity). As you approach maturity, both bonds will pull to par but the yield spread does not. For example let’s say both bonds are 1 yr maturity with 1% coupon. The risk free ... |
DW Industries has a D/E ratio of 0.5 and an ROE of 0.1. For every dollar it has in its assets, DW produces $0.2 in sales. In 2019, DW made all of its sales on credit with an average of $2million in Accounts Receivables. It took DW 30 days to collect the cash on purchases the clients made. What is your best estimate of ... |
DW Industries has a D/E ratio of 0.5 and an ROE of 0.1. For every dollar it has in its assets, DW produces \$0.2 in sales. In 2019, DW made all of its sales on credit with an average of \$2 million in Accounts Receivables. It took DW 30 days to collect the cash on purchases the clients made. What is your best estimate ... |
Assume we are calculating a value-weighted index of a set of stocks that have more or less the same capitalization. However, one of the stocks has substantially larger price than others (although market cap is still on the same level). For example:
```
Stock A: price 10, market cap 100 000
Stock B: price 15, market... |
I am trying to create a zero curve from a series of government bonds by minimizing the differences in the dirty prices.
The problem is that there is something wrong with my differential evolution algorithm.
My process is as follows:
1. I have utilized quantlib to generate the cash flow schedules and year fra... |
I am trying to create a zero curve from a series of government bonds by minimizing the differences in the dirty prices.
The problem is that there is something wrong with my differential evolution algorithm.
My process is as follows:
1. I have utilized quantlib to generate the cash flow schedules and year fra... |
Let's say I have 2 different and independent (can't be mixed) set of strikes, {K1} and {K2}. If I create a portfolio of options using the first set and calculate my payoff at expiration, would it be possible to replicate (or approximate) it with the other set of strikes {K2}?
I would appreciate too if you could shar... |
Is it possible to replicate the payoff of a portfolio of options taken from a set of strikes {K1}, given another set {K2} with the same underlying? |
Are Fama-French returns in percentages? |
I read the book "Theory of Games and Economic Behavior" by John von Neumann and Oskar Morgenstern. I think that stock market may be described by game theory. But here are the problems:
1. number of players (traders) varies. In this book that number is constant.
2. A player may act (e.g. place a limit order) whene... |
Could someone please explain to me how the calculation of the market expected FED rate hikes is done?
Thank you.[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/sFDBq.jpg |
I assume that you want to minimize the variance of the payoff error of your „hedge“.
Without loss of generality, let us assume that for some target strike level $K$ (from set 1), there exist $2n$ symmetrically (around $K$) spaced strikes in set 2, with spacing $\pm h,\pm2h,\pm3h...,\pm nh$. In order to minimize the... |
I assume that you want to minimize the variance of the payoff error of your „hedge“.
Without loss of generality, let us assume that for some target strike level $K$ (from set 1), there exist $2n$ symmetrically (around $K$) spaced strikes in set 2, with spacing $\pm h,\pm2h,\pm3h...,\pm nh$. In order to minimize the... |
I assume that you want to minimize the variance of the payoff error of your „hedge“.
Without loss of generality, let us assume that for some target strike level $K$ (from set 1), there exist $2n$ symmetrically (around $K$) spaced strikes in set 2, with spacing $\pm h,\pm2h,\pm3h...,\pm nh$. In order to minimize the... |
I assume that you want to minimize some error function of your replication. For simplicity, I will focus on the squared error integral below.
Without loss of generality, let us assume that for some target strike level $K$ (from set 1), there exist $2n$ symmetrically (around $K$) spaced strikes in set 2, with spacing... |
I've been going through the book "Fixed Income Securities" by Bruce Tuckman which gives the following definitions of the drift terms (after showing it for a specific example with 3 forward rate)
[![enter image description here][1]][1]
This expression includes the correlation between the forward rates.
To fin... |
I assume that you want to minimize some error function of your replication. For simplicity, I will focus on the squared error integral below.
Without loss of generality, let us assume that for some target strike level $K$ (from set 1), there exist $2n$ symmetrically (around $K$) spaced strikes in set 2, with spacing... |
Futures on dividends are directly related to the expected value of the dividends. A model for the dividends is not going to help in pricing of those futures - they are the hedging instruments.
For Options on dividends, early stochastic dividend models assume the dividend to be lognormal, see [Geske (1978)][1]. This... |
I would like to know if I can use maturity dates from my rates dataframe to generate OISratehelpers. In the following code the OIS rate helper use 'tenors' and I want to replace those tenors with maturity dates. For 'if' conditions, it is ok to use tenors but inside calculation I want to use maturity dates. I need help... |
QuantlIb: How to use maturities in place of Tenors in OIS rate helpers Quantlib? |
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