instruction stringlengths 15 26.1k |
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**Edit years later**: No idea why I'm upvoted. I actually don't get how I'm correct.
---
We are given a filtered probability space $(\Omega, \mathscr{F}, \{\mathscr{F}_t\}_{t \in [0,T]}, \mathbb{P})$, where $\{\mathscr{F}_t\}_{t \in [0,T]}$ is the filtration generated by standard $\mathbb P$-Brownian motion.
L... |
[Bayes' rule for conditional expectation][1] (or [here][2]) gives us
$$E_{\mathbb Q}[X_t | \mathscr F_u] E[L_T| \mathscr F_u] = E[X_tL_T| \mathscr F_u]$$
Use martingale property and iterated expectation:
$$E_{\mathbb Q}[X_t | \mathscr F_u] L_u = E[X_tL_T| \mathscr F_u]$$
$$= E[X_tE[L_T|\mathscr F_t]| \maths... |
**Edit years later**: No idea why I'm upvoted. I actually am not sure how I'm correct. But maybe I haven't forgotten conditional expectation as much as I thought I have.
---
We are given a filtered probability space $(\Omega, \mathscr{F}, \{\mathscr{F}_t\}_{t \in [0,T]}, \mathbb{P})$, where $\{\mathscr{F}_t\}_{t ... |
[Bayes' rule for conditional expectation][1] (or [here][2]) gives us
$$E_{\mathbb Q}[X_t | \mathscr F_u] E[L_T| \mathscr F_u] = E[X_tL_T| \mathscr F_u]$$
Use martingale property and iterated expectation:
$$E_{\mathbb Q}[X_t | \mathscr F_u] L_u = E[X_tL_T| \mathscr F_u]$$
$$= E[E[X_tL_T|\mathscr F_t]| \maths... |
The yahoo finance package (`yfinance`) in python is very nice, and for example:
msft = yf.ticker('MSFT')
msft.dividends
Will give the time series of historical ex-div dates for (in this case) `MSFT`. But what it does NOT give is the upcoming ex-div dates - obviously if some strategy requires doing some... |
I want to learn about Options Derivatives and am looking for an introductory (as much as possible) book to start with. Any recommendations? |
When solving for the minimum variance portfolio, we have the object:
$$
f(w) = \frac{1}{2} w^T \Sigma w
$$
subject to a basic scaling constraint:
$$
\sum_{i=1}^N w_i = 1
$$
or in matrix terms, $w^T \mathbf{1} = 1$ where $\mathbf{1}$ is the $n$ vector of all ones.
Forming the Lagrangian, we get:
$$
\S... |
I'm currently benchmarking several Monte Carlo computing methods for sensitivities computation purposes.
I've already done some implementation in Python using Numpy and MyGrad libraries and it's fascinating how fast it is.
Let's say that I have a C++ code that computes prices by Monte Carlo, how easy it is to imp... |
It is heard that trading wedges (cap/floor straddle - swaption) is actually trading the correlation btw forward rates. How to understand this? Either swaption or cap/floor seem to be insensitive to the correlation and that's one reason it is often suggested to calibrate correlation structure of LMM/HJM to CMS spread op... |
How to understand wedge? |
Usually, there is only one vol surface (I have never seen or heard of anyone using two). Almost certainly the most advanced commercially available vol surfaces are built by [voladynamics](https://voladynamics.com). They also offer only one surface for each underlying as well.
Even for interest rates, most of the t... |
I was wondering why ppl use the wordings being „rhs/LHS“ right hand side / left hand side when having an risk reversal for example Long EUR Call / USD Put and Short EUR Put / USD Call. Do they refer to the delta? and how do I know in which way to adjust the strike of the sold option in order to make it more valuable/ l... |
I have full order book data and I am writing a backtest for limit orders (to launch a new position not perofit taking or stop loss). I notice that this is actually a lot more difficult to write than a backtest for market orders because the backtest needs to take into account of when the limit order got hit and it could... |
https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html
We can see that the Winner and Loser portfolios are determined by the cumulative return from t-12 to t-2.
To construct the WML factor here, size(market cap) must also be considered.
What date's market capitalization should be considered?
... |
The Nelson-Siegel model as described in [this paper](http://web.math.ku.dk/~/rolf/teaching/NelsonSiegel.pdf) has the following form:
$$ y_t(\tau) = \beta_0 + \frac{(\beta_1+\beta_2)(1- e^{(-m/\tau)})}{\frac{m}{\tau}} - \beta_2e^{(-m/\tau)}
$$
Can the $\beta_s$ here be negative? Under what assumptions are they stri... |
Is it possible to have negative beta terms in the Nelson-Siegel model? |
> this is actually a lot more difficult to write than a
> backtest for market orders
This is to be expected. In my experience, the engineering difficulty and time goes up 1-2 orders of magnitude, because, among many things:
- On the market simulation side, you need
- full order book data, instead of BBO only;... |
Typically, the Actual price is derivative transaction (e.g. Swap) is sum of Base price and xVA e.g. cVA.
Where Base price is analytical price with consideration of standard parameters e.g. risk free rate for discounting future cash flows.
For simplicity, lets assume only valuation adjustment is considered as cVA,... |
I have never seen the *wedge* term in the literature, where do you get it from?
Caps and floors are indeed insensitive to correlation, since they are **baskets of options** (caplets/floorlets), but **this is not the case of swaptions**. Indeed, their single payoff at $T_\text{expiry}$ is
$$
\left[\sum\limits_{i = ... |
Hi I am trying to create a zero curve from continuous rates data. I keep getting an error "RuntimeError: two dates correspond to the same time under this curve's day count convention". What am I doing wrong? Identical function but replacing the daycount with ql.Thirty360 works fine. I also tried replacing compounding a... |
Reading:
https://quant.stackexchange.com/questions/1150/what-are-some-useful-approximations-to-the-black-scholes-formula
I understand that a ATM Call option can be approximated to $$ C(S,t)≈0.4Se^{−r(T−t)}σ \sqrt{T−t}$$
Also, I often hear that an ATM delta is around $\Delta = 0.5$.
However, using approximation fo... |
In short: the passed dates are converted into times, and the times are used to interpolate the passed rates. The conversion is done by taking the first passed date as `t=0`, and by assigning to each further date `d` the time `t = dayCounter.yearFraction(dates[0], d)`.
What is happening is that the act/act day count... |
I am trying to understand the mixing formula (Hull and White formula) for stochastic volatility models with jumps in the asset price. One article which discusses this is [Lewis, The mixing approach to stochastic volatility and jump models, Wilmott, 2002][1].
Is it correct to write the general stock price process in ... |
I am trying to understand the mixing formula (Hull and White formula) for stochastic volatility models with jumps in the asset price. One article which discusses this is [Lewis, The mixing approach to stochastic volatility and jump models, Wilmott, 2002][1].
Is it correct to write the general stock price process in ... |
This question concerns old LIBOR Swaps where their fixed legs are based on 30/360, and floating legs on Act/360.
Q1. Let's assume the simple self-discounting case where spot rates are obtained directly from the LIBOR swap curve itself. Can differences in day count conventions of the two legs lead to different "dis... |
What is the first known paper which derives the Black-Scholes valuation formula for an option (1973) using martingale machinery - instead of PDEs? |
Say I have quarterly returns data for a stock. I am currently calculating rolling Sharpe ratios using an eight-quarter forward window. So for example, say I have quarterly returns data starting in 2000Q1, then 2000Q2, 2000Q3, 2000Q4, etc.
What I do is take the arithmetic average of the quarterly returns from 2000Q1... |
How to annualize sharpe ratio using quarterly data? |
Assuming market-cap weights are all that matters (but not the exact market cap values), the easiest (free) way is probably to get the data from ETF holdings. ACWI is the ETF tracking MSCI ACWI. Here's some sample code to get the top 500 holdings:
data = pd.read_csv("https://www.ishares.com/us/products/239600/ish... |
> Q1. Let's assume the simple self-discounting case where spot rates are obtained directly from the LIBOR swap curve itself. Can differences in day count conventions of the two legs lead to different "discount factors" to use for each leg? (I am asking this because I've seen some educational websites that showed slight... |
> Q1. Let's assume the simple self-discounting case where spot rates are obtained directly from the LIBOR swap curve itself. Can differences in day count conventions of the two legs lead to different "discount factors" to use for each leg? (I am asking this because I've seen some educational websites that showed slight... |
> Q1. Let's assume the simple self-discounting case where spot rates are obtained directly from the LIBOR swap curve itself. Can differences in day count conventions of the two legs lead to different "discount factors" to use for each leg? (I am asking this because I've seen some educational websites that showed slight... |
Assuming market-cap weights are all that matters (but not the exact market cap values), the easiest (free) way is probably to get the data from ETF holdings. ACWI is the ETF tracking MSCI All Country World Index. Here's some sample code to get the top 500 holdings:
data = pd.read_csv("https://www.ishares.com/us/... |
The problem I am looking at concerns the treatment of almost identical assets in portfolio construction.
Let us assume that we have two assets, both with a standard deviation $\sigma=0.2$ and a correlation matrix
$$
C = \begin{pmatrix}
1 & 0.98 \\
0.98 & 1
\end{pmatrix}.
$$
One asset has a return of $\mu=0.... |
Below are some of the sources one can use to search for and view or download research articles and other publications on quantitative finance (QF). Many include non-peer-reviewed articles in their search results. Most carry or index articles in languages other than English.
The list of sources for any category is n... |
> Why is the required return assumed to be equal to the expected return?
Required return in a model depends on how you model agent's behavior and beliefs.
If you assume agents in a model consider CAPM the correct model of asset pricing, that is they all believe CAPM is the correct description of how returns shou... |
BCBS 261 sets specific rules regarding to the initial margin calculation for bilateral trade (https://www.bis.org/publ/bcbs261.pdf)
In page 21, the standardized rule sets the methodology for the same which is basically
Net Margin = (0.40 + 0.60 * NGR) * Gross Margin
Where `NGR` is the ratio of Net to gross... |
If we imposed the restriction that the strategy is not skewed, then using Chebyshev's Inequality I can show that the probability of it losing money in a year is less than 12.5%.
Let $X$ be the yearly PnL of a strategy. Let $\mathbf{E}(X) = \mu$ and $\mathbf{Var}(X)=\sigma$. We know that $\frac{\mu}{\sigma} = 2$.
... |
What can we say about the probability a strategy losing money in a year if it has an annualized Sharpe of say 2? |
In Section 2.5 of *Options, Futures, and Other Derivatives (8th edition)*, there is a paragraph discussing the credit risk associated with the operation of margins:
> The whole purpose of the margining system is to ensure that funds are available to pay
traders when they make a profit. Overall the system has be... |
How the margining system worked in this situation? |
I just want to be sure if my thinking is correct and does not have any flaws.
Let's define stock as a process $S$ (see the picture below) with real-world measure $\mathbb{P}$, where $p=0.9$ and Bonds with zero interest rate $r=0$.
[![process S][1]][1]
[1]: https://i.stack.imgur.com/sAZI1.png
Market Make... |
I just want to be sure if my thinking is correct and does not have any flaws.
Let's define stock as a process $S$ (see the picture below) with real-world measure $\mathbb{P}$, where $p=0.9$ and Bonds with zero interest rate $r=0$.
[![process S][1]][1]
[1]: https://i.stack.imgur.com/sAZI1.png
Market Make... |
I just accessed the [CME FedWatch Tool](https://www.cmegroup.com/markets/interest-rates/cme-fedwatch-tool.html?redirect=/trading/interest-rates/countdown-to-fomc.html) at 10:27am ET.
It reported mid price of ZQZ2 as 95.8788 and a corresponding probability of 74.7% of 50bp hike at Dec FOMC meting (vs 75bp).
For De... |
I am trying to calibrate a Vasicek model given by
$$
dr(t) = k[\theta - r(t)] dt + \sigma dW(t), \quad r(0) = r_0
$$
where $k, \theta, \sigma, r_0 > 0$. I am using the book by Brigo and Mercurio.
I found many resources online and in the book on how to estimate the parameters, given some sample data $r_1, \dots... |
How does one calibrate a Vasicek model to actual cap prices? |
As I know a `CDS` is defined w.r.t. some unique Reference bond with a given maturity from a given issuer. Now, an issuer can issue bonds with different maturities and notionals. So, how are the Notional values of the underlying bonds normalized, if at all, in order to construct a term structure of CDS spread from an is... |
I want to price gov bonds using the Bid Yield rates from the screen below, and quantlib.
I am not sure what those Bid Yield rates represent.
Are they spot rates or par yields?
If spot rates I can just plug them in, but if those are par yields I should bootstrap spot rates.
[![enter image description here][1]][1... |
I want to price gov bonds using Bid Yields from the screen below, and quantlib.
I am not sure what those Bid Yield rates represent.
Are they spot rates or par yields?
If spot rates I can just plug them in, but if those are par yields I should bootstrap spot rates.
[![enter image description here][1]][1]
... |
I want to price gov bonds using Bid Yields (column 5) from the screen below, and quantlib.
I am not sure what those Bid Yield rates represent.
Do those Bid yields represent spot rates or par yields?
If spot rates I can just plug them in, but if those are par yields I should bootstrap spot rates.
[![enter image ... |
I want to price gov bonds using Bid Yields (column 5) from the screen below, and quantlib.
I am not sure what those Bid Yield rates represent.
Do those Bid yields represent spot rates, or what?
[![enter image description here][1]][1]
[1]: https://i.stack.imgur.com/5Te6y.jpg |
How is call theta mathematically derived from Black Scholes Model (without approximation) ? Please help me understand each step mathematically. |
I have an intraday strategy, which will place 0-5 trades for each intraday trading session. (Note that some days it will not place any trades out). The average duration of a trade is around 33 minutes.
From my understanding, the sharpe ratio formula is calculated as mean of excess return of all the trades divided s... |
I have an intraday strategy, which will place 0-5 trades for each intraday trading session. (Note that some days it will not place any trades out). The average duration of a trade is around 33 minutes.
From my understanding, the sharpe ratio formula is calculated as mean of excess return of all the trades divided s... |
I would like to use the Black Scholes model to get the strike based on delta, **without having to guess the option price**.
So I read this: https://quant.stackexchange.com/questions/33590/from-delta-to-moneyness-or-strike
Which show that we can get a strike price with :
=()−(−1(Δ)+1/2)−√T-t
But with ... |
I would like to use the Black Scholes model to get the strike based on delta, **without having the option price**.
So I read this: https://quant.stackexchange.com/questions/33590/from-delta-to-moneyness-or-strike
Which show that we can get a strike price with :
=()−(−1(Δ)+1/2)−√T-t
But with this my s... |
Let's suppose we work for a Vanilla Call Option.
The formula for Delta is :
$\Delta = \frac{\partial V}{\partial S} = N(d1)$
where $d1 = \frac{ln(\frac{S}{K})+(r + \frac{\sigma^2}{2})t}{\sigma \sqrt(t)}$
and $N(x)$ is the Standard normal cumulative distribution function.
Now, given the value of Delta, you c... |
Let $V_t^{T_1, T_2}$ be the forward variance swap rate for the period $[T_1, T_2]$, seen from $t$ (see for instance Lorenzo Bergomi's [Smile Dynamics II][1]) and let $\xi_t^T = V_t^{T,T} = \frac{\partial}{\partial T} V_t^T$ be the instantaneous forward variance swap rate at $T$ seen from $t$, where $$V_t^T = P_{t,T} \m... |
Let $V_t^{T_1, T_2}$ be the forward variance swap rate for the period $[T_1, T_2]$, seen from $t$ (see for instance Lorenzo Bergomi's [Smile Dynamics II][1]) and let $\xi_t^T = V_t^{T,T} = \frac{\partial}{\partial T} V_t^T$ be the instantaneous forward variance swap rate at $T$ seen from $t$, where $$V_t^T = P_{t,T} \m... |
I have a dataframe with a list of numbers in column A in Python, and I would like to get the two closest numbers in this list to a specific number X. Does anyone know how to do this? |
The first terms are duration and convexity, but are there common names for the terms beyond this? |
Are there names from the third term onwards in the Taylor approximation for bond pricing? |
I was wondering if there are recurring puzzles in the area of quant finance / finance published by the industry similar to [ponder this of IBM Research][1]?
[1]: https://research.ibm.com/haifa/ponderthis/index.shtml |
Lets consider the simple interest rate swap instrument as 5-year maturity interest rate swap. I found an interesting simplification to calculate the duration of such swap as,
$\frac{\left(1 - e^{-r_t * T}\right)}{r_t}$
In above expression the $r_t$ is current level of interest rate and $T$ is the swap maturity i.... |
Let $V_t^{T_1, T_2}$ be the forward variance swap rate for the period $[T_1, T_2]$, seen from $t$ (see for instance Lorenzo Bergomi's [Smile Dynamics II][1]) and let $\xi_t^T = V_t^{T,T} = \frac{\partial}{\partial T} V_t^T$ be the instantaneous forward variance swap rate at $T$ seen from $t$, where $$V_t^T = P_{t,T} \m... |
Let $V_t^{T_1, T_2}$ be the forward variance swap rate for the period $[T_1, T_2]$, seen from $t$ (see for instance Lorenzo Bergomi's [Smile Dynamics II][1]) and let $\xi_t^T = V_t^{T,T} = \frac{\partial}{\partial T} V_t^T$ be the instantaneous forward variance swap rate at $T$ seen from $t$, where $$V_t^T = P_{t,T} \m... |
Let $V_t^{T_1, T_2}$ be the forward variance swap rate for the period $[T_1, T_2]$, seen from $t$ (see for instance Lorenzo Bergomi's [Smile Dynamics II][1]) and let $\xi_t^T = V_t^{T,T} = \frac{\partial}{\partial T} V_t^T$ be the instantaneous forward variance swap rate at $T$ seen from $t$, where $$V_t^T = P_{t,T} \m... |
Are there two definitions to Flow Trading? From reading online, I've gathered two, but I'm not sure if I am mistaken, so a little bit of clarification would be very much appreciated.
(1) Flow Trading - trading that uses clients' money (I would assume something like a hedge fund)
(2) Flow Trading - same as market ... |
What is the difference between Flow Trading and Market Making? |
Let us consider that we are looking at issuing some varswaps or volswaps on some FX rate. By longer term I mean something longer than 3 months. Different from this time two years ago, now the interest rates are much more volatile. Is there a paper detailing how stochastic rates impact the valuation of varswaps and vols... |
I am new to exotic options pricing and risk management. The scenario that I encounter is that the market maker sells snowball autocallable products(accumulated coupon) every trading day and has to manage a big portfolio that is heterogeneous in underlying asset, time to maturity, strikes(both knock-in and knock-out). B... |
I can't post this as a comment yet (not enough reputation), but for the impact of stoch rates on varswaps you can take a look at his:
[Horfelt & Torne, The value of a variance swap - a question of interest][1]
[1]: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1469533 |
How does a bank assess the liquidity of OTC derivatives such as swaps, options, and forwards, for which there isn't public data regarding trading volume? |
I create a vol surface from the market and do smoothing(interpolation and extrapolation), and explicitly correct for any total variance decreasing on a given strike as we increase maturity. I create a ql.BlackVarianceSurface surface with my grid and am able to price using most quantlib engines. When I use my surface to... |
Suppose I have a bond, with a face value of 95, a coupon of 2%, and a maturity of 50 years. Suppose the discount curve is flat at 2%, and there is no credit spread.
I am trying to calculate what happens when the credit/ interest rates change.
For example, how can I revalue the bond if the credit spread increases ... |
I have an intraday strategy, which will place 0-5 trades for each intraday trading session. (Note that some days it will not place any trades out). The average duration of a trade is around 33 minutes.
From my understanding, the sharpe ratio formula is calculated as mean of excess return of all the trades divided s... |
I have yields for UK index-linked bonds with particular maturity dates.
e.g "Maturity": "26/01/2035" and "Yield": "-0,129875"
I want to calculate the breakeven rate for that particular bond.
The data I have for government bond yields is for benchmark gilts.
e.g "Tenor": 15Y and "Yield": 3.081%
To calculat... |
How to calculate the breakeven rate for a UK index-linked bond? |
From your linked article at the SEC,
>the "Quote Rule" and the "Limit Order Display Rule," aim to increase the information that is publicly available
The market makers must honor their quotes (and other participants must honor their open limit orders). The failure to do so in the crash of 1987 brought about the "... |
To Problem 2.22 in *Options, Futures, and Other Derivatives* (8th edition) below:
> *When a futures contract is traded on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one." Explain this statement.*
the Solution is:
> If both sides of the ... |
There seems to some confusion about the language. The book is referring to trades that are all on the same futures contract , just done at different times and different prices. So when it says ‘new contract’ it should really say ‘new trade on the same contract ‘. Then it should become obvious. If you are long 1 cont... |
I am trying to derive a Stock Price Distribution for a particular time frame. Meaning thereby, let's say Market is about to close in 30 minutes and I want to calculate Stock Price Distribution for the opening of the next day. I have read some of the research paper(s), in which they have said that by double differentiat... |
How to calculate YTM of AmortizingFixedRateBond in QuantLib - Python? |
Typically physical assets e.g. gold are held as collateral for corporate loan. In case of default, the holder of the corporate loan (i.e. bank) can liquidate the collateral asset held to recover the principal and other expenses.
My question is what is the tax implication for such selling of collateral, assuming valu... |
> Given the share price equation
$$
dS_t=rS_tdt+\sigma S_tdW_t
$$
working in the framework of Black-Scholes model, find the price at $t=0$ of the following two financial assets:
>
>(a) The asset pays at $t=T$ exactly $S_T^2$.
>
>(b) The asset pays at $t=T$ exactly $1$ if $S_T<K$, where $K$ is constant specified... |
I have:
- zero coupon 3M,6M,1Y,2Y,3Y....bond yields
- 1W,2W,1M,2M,3M.... bill yields
To build a yield curve what is better:
1. build a single curve combining bond+bill yields, and price bonds and bills using that 1 curve
2. build 2 separate yield curves, 1 to price bonds use a curve made of the bond yields, an... |
I have:
- zero coupon 3M,6M,1Y,2Y,3Y....bond yields
- 1W,2W,1M,2M,3M.... bill yields
To build the yield curve what is better:
1. build a single curve combining bond+bill yields, and price bonds and bills using that 1 curve
2. build 2 separate yield curves, 1 to price bonds use a curve made of the bond yields, ... |
I have:
- zero coupon 3M,6M,1Y,2Y,3Y....bond yields
- 1W,2W,1M,2M,3M.... bill yields
To build the yield curve what is better:
1. build a single curve combining bond+bill yields, and price bonds and bills using that 1 curve
2. build 2 separate yield curves, 1 to price bonds use a curve made of the bond yields, ... |
Construct yield curve using ZC bond and bill yields or bond yields only? |
I have:
- 3M,6M,1Y,2Y,3Y....bonds
- 1W,2W,1M,2M,3M.... bills
To build the yield curve what is better:
1. build a single curve using bonds+bills
2. build 2 separate yield curves, 1 to price bonds made out of bonds only, and to price bills, bill only curve
3. something else?
EDIT just to clarify, I am con... |
Construct yield curve using bonds and bills or bonds only? |
I was told that a Cross currency swap can be thought of as a portfolio of 2 different interest rate swaps.
Can you please help me to understand intuitively how this is the case? Typically, in Interest rate swap, we have fixed leg and floating leg in same currency. In Cross current swaps cash flows the exchanged in d... |
There seems to some confusion about the language. The book is referring to trades that are all on the same futures contract , just done at different times and different prices. So when it says ‘new contract’ it should really say ‘new trade on the same contract ‘. Then it should become obvious. If you are long 1 cont... |
**Basic question:**
Can we generalize the HJB PDE to apply to optimal controls of non-Markovian/path-dependent SDEs? Specifically, how do we generalize the log-optimal portfolio to path-dependent processes?
Skip down below to the Main-Question/Goal for more details if you are familiar with this background of stoc... |
I think this is the intuitive way to think about specialness in bond futures, at least to my mind; therefore, I am wondering if my logic is correct:
Cash Bonds have a forward price that is totally deterministic today based on its carry, which is income - financing + any pull to par. This is the actual no-arbitrage f... |
I was told that a Cross currency swap can be thought of as a portfolio of 2 different interest rate swaps.
Reference link : https://cvacentral.com/wp-content/uploads/2020/06/Chapter-11-Appendices-4E.pdf (page 4)
Can you please help me to understand intuitively how this is the case? Typically, in Interest rate swa... |
I'm helping my team to project 90-day T-bill forward rates. I have two options: using FWCM or FWCV in Bloomberg. My team has used FWCM. Today I opened FWCV and found that the rates for the same curve (US Treasury Actives Curve) are not the same.
FWCM:
[![FWCM][1]][1]
FWCV:
[![FWCV][2]][2]
I contacted Bloombe... |
You missed to mention a lot of details in your link.
- Firstly, the XCCY Swap is said to be an approximation of an FX forward and swaps, not just swaps.
- Secondly, the FX swap is approximated.
- Thirdly, the swaps are approximated, assuming a flat yield curve (which is never the case).
- It is for approximating... |
You missed to mention a lot of details in your link.
- Firstly, the XCCY Swap is said to be an approximation of an FX forward and swaps, not just swaps.
- Secondly, the FX swap is approximated.
- Thirdly, the swaps are approximated, assuming a flat yield curve (which is never the case).
- It is for approximating... |
I understand the first order MG of brownian motion is Bt.. the second order is Bt^2 - t and the third order is bt^3 - 3tBt. How can I find the fourth and beyond order of a Brownian Motion Martingale? |
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