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**Problem** I am considering an American call option which gives a domestic investor the right to buy a unit of foreign currency at a strike of $K$ units of domestic currency. I have an exchange rate $S_t$ in units of domestic to foreign currency which follows $$\frac{\mathrm{d}S_t}{S_t}=\mu\mathrm{d}t+\sigma\mathrm{d...
Brooks - *Introductory Econometrics for Finance* is a very comprehensive, accessible overview of all the mainstream models for capturing non-normality, serial correlation, non-stationarity and other properties of financial returns, data, and volatility, bundled with plenty of reproducible examples. Another accessib...
I am trying to value a real option in the form of a software investment using a simulation. The software investment yields to daily revenues $R_t$ and costs $C_t$. Here are the formulas for these: $$R_t=a+E_t*b$$ $$C_t=c*O_t$$ $a, b$ and $c$ are constants, $E_t$ is a daily changing exchange rate and $O_t$ is a...
Other than the books described by @develarist, there are also some alternative considerations which I have grouped into overall subjects: **Financial econometrics/Financial modelling:** - *Analysis of Financial Time-Series by Ruey S. Tsay*. The book gives you a comprehensive introduction to econometric modelling...
I am considering a fund that replicates the returns of an index minus a fee. Denoting the price of the index as $X_t$ and the price of one unit in the fund as $Y_t$, I model the transaction costs in continuous time such that $$Y_t=X_t\mathrm{e}^{-kt},\quad k>0.$$ Is the futures price on $Y_t$ just naively $$F_{t,T}=Y...
I have to build a classification model to predict recessions. I have selected a set of features (some are economic and some are financial). I have noticed that it is good pratice often to add to the original features also their lagged versions. So basically the features are lagged/shifted forward in the "future" of ...
**Problem** I am considering an American call option which gives a domestic investor the right to buy a unit of foreign currency at a strike of $K$ units of domestic currency. I have an exchange rate $S_t$ in units of domestic to foreign currency which follows $$\frac{\mathrm{d}S_t}{S_t}=\mu\mathrm{d}t+\sigma\mathrm{d...
I am considering a fund that replicates the returns of an index minus a fee, using the following case-study my lecturer tried to explain to me using SPY: > In practice, futures and forwards can be written on assets which are > not directly tradeable. Consider the E-mini futures contract example > on the S&P 500 index,...
Let $f(S)$ denote the (initial) value of a call option with underlying spot price $S$. I assume that the underlying has continuous sample paths. As $S\to\infty$, we know that $f=\mathcal{O}(S)$ (using [big O notation][1]) because the option is essentially linear in the underlying ($\Delta=1$ and $\Gamma=0$ for deep ...
I would like to understand the math/economics behind the calculation of plain vanilla FX forwards. Let's assume the following example: ``` - The deal is traded on 2021.01.01 (t=0) - Party A agrees to buy 1.000.000 CAD and sell 800.000 USD on June 30th 2021 - The CAD riskfree interest rate is 0.50 % p.a. -...
Not sure this answers your question, but the speed at which the option prices changes with respect to the underlying is the delta, which is just equal to $N(d_1)$, with $d_1$: $$d_1=\frac{ln\left(\frac{S}{K}\right)+rt+0.5\sigma^2t}{\sigma \sqrt{t}}$$ As $S \to 0$, $ln\left(\frac{S}{K}\right) \to (-\infty)$, and t...
Not sure this answers your question, but the speed at which the option prices changes with respect to the underlying is the delta, which is just equal to $N(d_1)$, with $d_1$: $$d_1=\frac{ln\left(\frac{S}{K}\right)+rt+0.5\sigma^2t}{\sigma \sqrt{t}}$$ As $S \to 0$, $ln\left(\frac{S}{K}\right) \to (-\infty)$, and t...
As per title, where would I find the latest research papers on modeling option pricing, accounting for IV smile? I'm specifically interested in papers that already found practical application in some form by any trading firms, or may be considered by, or recommended to them. I'd also be interested in any practical im...
Let $C(S)$ denote the (initial) value of a call option with underlying spot price $S$. I assume that the underlying has continuous sample paths (not necessarily a geometric Brownian motion though). As $S\to\infty$, we know that $C=\mathcal{O}(S)$ (using [big O notation][1]) because the option is essentially linear i...
[Brooks - *Introductory Econometrics for Finance*][1] is a very comprehensive, accessible overview of all the mainstream models for capturing non-normality, serial correlation, non-stationarity and other properties of financial returns, data, and volatility, bundled with plenty of reproducible examples. [Mills and ...
I am considering a fund that replicates the returns of an index minus a fee, using the following case-study my lecturer used regarding SPY: > In practice, futures and forwards can be written on assets which are > not directly tradeable. Consider the E-mini futures contract example > on the S&P 500 index, where due to ...
*Edit*: the original question didn't specify "model independence" and so the below focuses on the BS framework. Also, i focused on *speed of convergence* rather than *order of convergence*: I will try to update my answer with some thoughts on *order of convergence* later on. Not sure this answers your question, but ...
My questions is the following: why is it that the modified duration can explain so well the change in price of bonds? I don't get the mathematical relationship behind this, that is between modified duration and the percentage change in price of the bond that it predicts. Can anyone give me the intuition behind this? Th...
How do limit order prices meet?
Bond price in terms of yield (denoted "$y$") is just the Present Value (PV) of the Bond coupons (denoted "$C$") and the final Notional (denoted $N$), discounted at the yield. Suppose the bond matures in 10 years time, then the present value can be written as (yields expressed as annualized for simplicity): $$PV=\sum...
I have some difficulty understanding the following proof and I hope someone can help me with that. **Claim:** I want to show that $E_\alpha(S)=\frac{d}{dr} \log M_S(r)|_{r=\alpha} $, where $M_S(r)=E(\exp(rS))$ is the moment generating function of $S\sim F$ and $E_\alpha(S)=\int_{\mathbb{R}} s dF_\alpha(s)$ with...
I need to forecast non-maturity deposits in a bank. My intent is to use Recurrent Neural Networks (aka deep learning) to model time series. The model will learn from past bank data and macroeconomic variables, and forecast deposits in the next three years based on projected variables. Two questions: 1. Do you...
I have some difficulty understanding the following proof and I hope someone can help me with that. **Claim:** I want to show that $E_\alpha(S)=\frac{d}{dr} \log M_S(r)|_{r=\alpha} $, where $M_S(r)=E(\exp(rS))$ is the moment generating function of $S\sim F$ and $E_\alpha(S)=\int_{\mathbb{R}} s dF_\alpha(s)$ with...
I would like to understand in which case there is a presence of FX delta risk factor when trading a Cross-currency basis swap. By FX Delta, I mean the sensitivy of my swap PV with respect to FX Spot moves. Let’s consider those cases : 1. Standard Xccy basis (float/ float) with USD leg resettable. Initial and ...
**Problem** I am considering an American call option which gives a domestic investor the right to buy a unit of foreign currency at a strike of $K$ units of domestic currency. I have an exchange rate $S_t$ in units of domestic to foreign currency which follows $$\frac{\mathrm{d}S_t}{S_t}=\mu\mathrm{d}t+\sigma\mathrm{d...
I am considering a fund that replicates the returns of an index minus a fee, using the following case-study my lecturer used regarding SPY: > In practice, futures and forwards can be written on assets which are > not directly tradeable. Consider the E-mini futures contract example > on the S&P 500 index, where due to ...
Responding to the first question and building on Dimitri's comments, it is probably worth your while to do some due-diligence on the some of the standard issues that come up in Financial ML and see to what extent they apply to your problem: 1. Interpretability: How will you interpret the results of your Deep Learni...
Responding to the first question and building on Dimitri's comments, it is probably worth your while to do some due-diligence on the some of the standard issues that come up in Financial ML and see to what extent they apply to your problem: 1. Interpretability: How will you interpret the results of your Deep Learni...
I've been struggling to find engaging papers on the utilization of deep reinforcement learning in either quantitative risk analysis, portfolio management, algorithmic trading or options pricing. What are some papers with interesting findings on this topic that you know of? Thanks in advance!
Use of Reinforcement Learning in Quant Finance Papers?
How do we price an American Put Option with simplified assumptions of non-zero interest rate but zero volatility and zero dividend rate? I understand the concept of Perpetual American Options and I know we need to find optimal boundary constraints. But I fail to understand how we can price the Perpetual American Put...
How to price a Perpetual American Put Option with the Binomial Tree Model?
You can find a lot of good papers by just typing keywords like "deep reinforcement learning finance" in the arXiv or Google Scholar or looking at top researchers websites which provides an overflow of applications and research directions to engage with. Anyway, here are a few off the top of my head: If you are looki...
You can find a lot of good papers by just typing keywords like "deep reinforcement learning finance" in the arXiv or Google Scholar or looking at top researchers websites which provides an overflow of applications and research directions to engage with. Anyway, here are a few off the top of my head: If you are looki...
You can find a lot of good papers by just typing keywords like "deep reinforcement learning finance" in the arXiv or Google Scholar or looking at top researchers websites which provides an overflow of applications and research directions to engage with. Anyway, here are a few off the top of my head: If you are looki...
You can find a lot of good papers by just typing keywords like "deep reinforcement learning finance" in the arXiv or Google Scholar or looking at top researchers websites which provides an overflow of applications and research directions to engage with. Anyway, here are a few off the top of my head: If you are looki...
Pine script that could be applied on tradingview: ``` study(title="RSI Divergence_alper", shorttitle="RSI Divergence_alper") src_fast = close, len_fast = input(5, minval=1, title="Length Fast RSI") src_slow = close, len_slow = input(14,minval=1, title="Length Slow RSI") up_fast = rma(max(change(src_fast), 0), le...
Pine script that could be applied on tradingview, [reference][1]: ``` study(title="RSI Divergence", shorttitle="RSI Divergence_alper") src_fast = close, len_fast = input(5, minval=1, title="Length Fast RSI") src_slow = close, len_slow = input(14,minval=1, title="Length Slow RSI") up_fast = rma(max(change(src_fas...
You can find a lot of good papers by just typing keywords like "deep reinforcement learning finance" in the arXiv or Google Scholar or looking at top researchers websites which provides an overflow of applications and research directions to engage with. Anyway, here are a few off the top of my head: If you are looki...
After reading papers on reinforcement learning with respect to the problem of optimal execution (Nevmyvaka et al (2006), Ning et al (2018), etc), I was wondering if the Markov property assumed in all these papers is rational? Has there been at least an empirical comparison/paper detailing tradeoffs & performance of non...
You can find a lot of good papers by just typing keywords like "deep reinforcement learning finance" in the arXiv or Google Scholar or looking at top researchers websites which provides an overflow of applications and research directions to engage with. Anyway, here are a few off the top of my head: If you are looki...
How would a rise in implied volatility on a short-term option affect the implied volatility of another short-term option with the same strike, but with slightly-longer expiry? Assuming that the short-term volatility rise is due to an event completely contained in the time of the short-term option. Here is my sta...
I am conducting PCA on several return series of funds and am finding that when I look at the first principal component the values are huge and this the volatility is also enormous relative to the funds I have used to construct the PCA. The average return vol for the funds is 3.38% with the largest being roughly 5%....
I've been struggling to find engaging papers on the application of deep reinforcement learning in quantitative risk analysis, portfolio management, algorithmic trading and/or options pricing. What are some papers with interesting findings on this topic that you know of?
Deep Reinforcement Learning in Quant Finance?
How to find the volatility of an asset in a Binomial Tree Model? Suppose the price of the Stock is $S_t$ at time $t$ and it has a probability of $p$ that will go up $u$ times to $u \cdot S_t$ and a probability $(1-)p$ that it will go down to $d \cdot S_t$ at time $t+1$. And this goes on indefinitely. [![enter image d...
How to find volatility of an infinitely expanding Binomial Tree?
How to find the volatility of an asset in a Binomial Tree Model? Suppose the price of the Stock is $S_t$ at time $t$ and it has a probability of $p$ that will go up $u$ times to $u \cdot S_t$ and a probability $(1-p)$ that it will go down to $d \cdot S_t$ at time $t+1$. And this goes on indefinitely. [![enter image d...
Is there an equivalent to implied volatility used when it comes to modelling correlation in option valuation for multi asset options such as rainbow options (best-of/worst-of calls/put), or is the best you can do to model the real world sample correlation of the time-series of the assets (or something other that I'm no...
I have a basic question regarding B_S_M formula, would be thankful for any assistance. As far as I understand N(d2) & N(-d2) stand for the probability of an option being exercised, Call & Put in accordance. If so, isn't 2 adjacent same type options with the same expiry must have a difference in premiums of at lea...
Pine script that could be applied on tradingview, [reference][1]: ``` study(title="RSI Divergence", shorttitle="RSI Divergence_alper") src_fast = close, len_fast = input(5, minval=1, title="Length Fast RSI") src_slow = close, len_slow = input(14,minval=1, title="Length Slow RSI") up_fast = rma(max(change(src_fas...
How to find the price variance of an asset in a Binomial Tree Model? Suppose the price of the Stock is $S_t$ at time $t$ and it has a probability of $p$ that will go up $u$ times to $u \cdot S_t$ and a probability $(1-p)$ that it will go down to $d \cdot S_t$ at time $t+1$. And this goes on indefinitely. [![enter ima...
How to find the price variance of an infinitely expanding Binomial Tree?
I have a basic question regarding B_S_M formula, would be thankful for any assistance. As far as I understand $N(d2)$ & $N(-d2)$ stand for the probability of an option being exercised, Call & Put in accordance. If so, isn't 2 adjacent same type options with the same expiry must have a difference in premiums of at...
I have a basic question regarding the BSM formula, would be thankful for any assistance. As far as I understand $N(d2)$ and $N(-d2)$ stand for the probability of a Call and Put respectively being exercised. If so, isn't it the case that two adjacent same type options with the same expiry must have a difference in...
Suppose a 3% 10-year bond is trading at 89 and a 7% 10-year bond is trading at 97. Then (assuming no arbitrage) the price of a 10-year zero-coupon bond would be: The answer should be 83. How using only cash- flows (no excel formulas) I would be able to get 83? When I multiply the price of the first cashflow by se...
I am running a PCA on a set of returns and I would like to cluster the results of the output to group stocks that have similar factor exposures. However when I run the PCA on the covariance of the returns, the PCA score (values mapped to new plane of PCs) gives me a matrix with dates and the principal components, ...
This boils down to timeseries forecasting which is particularly challenging for financial data because finance exhibits all the things that makes forecasting hard: non stationary, low signal to noise, etc. In the case of forecasting deposits, I very much doubt that you will be able to get satisfactory results even i...
This boils down to timeseries forecasting which is particularly challenging for financial data because finance exhibits all the things that makes forecasting hard: non stationary, low signal to noise, etc. In the case of forecasting deposits, I very much doubt that you will be able to get satisfactory results even i...
What difference do they make? Why do many people seem to find more accurate simulations with log volatility?
What is the difference between log volatility and simple volatility in a GBM?
In the binomial pricing model, why do the magnitude of the up factor (u) and down factor (d) have to be multiplicative inverses? I have read from multiple sources that the reason for this is that an up move followed by a down move (ud) will have the same effect as a down move followed by an up move (du), which simplifi...
Newbie here and not trading IRL but for a school assignment. I want to buy corporate bonds because they are a safe bet from what I read. I have a few questions though, I hope I will find an answer here: Can I sell them after one month? If yes, will I still get the bond yield/12? And finally, how much the interest...
I often see Vega in the Heston model specified as: \begin{align*} \nu & = \frac{\partial C}{\partial v} = \frac{\partial C}{\partial v_0} 2 \sqrt{v_0} \end{align*} where $v = \sqrt{v_0}$. Why are we setting $v = \sqrt{v_0}$? Where is the square-root and "2" coming from? Thank you!
Calculating vega in Heston?
I am wondering what the term S means in the equation I have circled? I am not sure how to interpret it. [![enter image description here][1]][1] [1]: https://i.stack.imgur.com/j0rbG.png
>Can I sell them after one month? Probably - it depends on what type of bond and how liquid (easy to sell) it is. >If yes, will I still get the bond yield/12? Maybe - but more than likely you'll sell it for more or less than what you paid for it. You _do_ get whatever interest accrues between the time you bou...
"how much the interest rates fluctuate in a month?" If you mean the yields (i.e. Treasury rate + credit spread) or just Treasury rates then you can download some corporate bond index data here: https://fred.stlouisfed.org/searchresults/?st=OAS.
>Can I sell them after one month? Probably - it depends on what type of bond and how liquid (easy to sell) it is. >If yes, will I still get the bond yield/12? Maybe - but more than likely you'll sell it for more or less than what you paid for it. You _do_ get whatever interest accrues between the time you bou...
I am trying to price the Asian lookback option at time $t$ with time-$T$ (European) payoff $\max\{M_T-A_T,0\}$, where $$M_t=\max_{u\in[0,t]}S_u,\quad A_t=\frac1t\sqrt{\int_0^tS_u^2\mathrm{d}u},$$ and $S_u$ is the price of an asset following GBM. How does one price such a formula? Is it correct to expect $V_t(t, s, m, i...
I often see Vega in the Heston model specified as: \begin{align*} \nu & = \frac{\partial C}{\partial v} = \frac{\partial C}{\partial v_0} 2 \sqrt{v_0} \end{align*} where $v = \sqrt{v_0}$. Why are we setting $v = \sqrt{v_0}$? Where is the square-root and "$2$" coming from?
Interesting choice, for a school project. If you want to get an idea for how much these things usually don't but sometimes can and do move around, have a look at LQD or HYG/JNK, these being respectively the "investment grade" (ie duller) and "high yield" (ie riskier) universes. The "yield" you're seeing is what you...
I have to build a classification model to predict recessions. I have selected a set of features (some are economic and some are financial). I have noticed that it is good pratice often to add to the original features also their lagged versions. So basically the features are lagged/shifted forward in the "future" of ...
I am trying to price the Asian lookback option at time $t$ with time-$T$ (European) payoff $\max\{M_T-A_T,0\}$, where $$M_t=\max_{u\in[0,t]}S_u,\quad A_t=\frac1t\sqrt{\int_0^tS_u^2\mathrm{d}u},$$ and $S_u$ is the price of an asset following GBM. How does one price such a formula? Is it correct to expect $V_t(t, s, m, i...
I have run a PCA on some returns to get a set of factors. All is good except that the first PC seems to be the short of the market, it has a correlation of -0.9 with the S&P500 but all the loadings are negative (except one which is very small and basically +0). I am confused as to why the PC is negative and all the...
Suppose that the current spot rate curve (annually compounded) is s1=0.2%, s2=0.8%, s3=1.2%. Assume that one year from now, the spot rate curve will be s'1=0.8%, s'2=1.4%, s'3=1.8%. Consider a 3-year bond with annual coupon 5%. If you purchase that bond today and hold it for one year, what will be your total retu...
I am trying to price the Asian lookback option at time $t$ with time-$T$ (European) payoff $\max\{M_T-A_T,0\}$, where $$M_t=\max_{u\in[0,t]}S_u,\quad A_t=\frac1t\sqrt{\int_0^tS_u^2\mathrm{d}u},$$ and $S_u$ is the price of an asset following GBM. How does one price such a formula? Is it correct to expect $V_t(t, s, m, ...
Exotic options, in general, have very time-consuming valuation models. I believe in recent years there has been some research done on using supervised machine/deep learning to predict the valuation given a training set of valuation done using traditional methods and other training features like greeks, market data etc....
What difference do they make? Why do many people seem to find more accurate simulations with log volatility? standard volatility in GBM is defined as $\sigma = \frac{1}{N}\sum_{i=1}^N(x_i-\mu)$ where $x_i$ is the rate of return and $\mu$ is the mean of the rate of return, also called the drift. Log volatitily on the...
What difference do they make? Why do many people seem to find more accurate simulations with log volatility? standard volatility in GBM is defined as $\sigma = \frac{1}{N}\sum_{i=1}^N(x_i-\mu)$ where $x_i$ is the rate of return and $\mu$ is the mean of the rate of return, also called the drift. Log volatitily on the...
I am trying to price the Asian lookback option at time $t$ with time-$T$ (European) payoff $\max\{M_T-A_T,0\}$, where $$M_t=\max_{u\in[0,t]}S_u,\quad A_t=\frac1t\sqrt{\int_0^tS_u^2\mathrm{d}u},$$ and $S_u$ is the price of an asset following GBM. How does one price such a formula? What can we do to show that $V_t(t, s,...
In the binomial pricing model, why do the magnitude of the up factor $(u)$ and down factor $(d)$ have to be multiplicative inverses? I have read from multiple sources that the reason for this is that an up move followed by a down move $(ud)$ will have the same effect as a down move followed by an up move $(du)$, which ...
What difference do they make? Why do many people seem to find more accurate simulations with log volatility? standard volatility in GBM is defined as $\sigma = \frac{1}{N}\sum_{i=1}^N(x_i-\mu)$ where $x_i$ is the rate of return and $\mu$ is the mean of the rate of return, also called the drift. Log volatitily on the...
In its simplest form, the difference is "variance drag", ie how volatility itself affects your mu above. Imagine a series of random returns of +50% versus -50% with a 50% probability of each. Evidently this will have a mu of zero, and a sigma of 0.5. But if prices halve and appreciate by 50% with equal probabil...
You can find a lot of good papers by just typing keywords like "deep reinforcement learning finance" in the arXiv or Google Scholar or looking at top researchers websites which provides an overflow of applications and research directions to engage with. Anyway, here are a few off the top of my head: If you are looki...
The probability distribution used for mortgage backed securities divided them into tranches. If tranch#1 was worth 10 million USD, they got paid in full while the rest got paid partially. Most of them defaulted. What was the probability distribution used? And what is the statistics behind what they did?
What is the probability distribution used for mortgage backed securities during the subprime crisis?
I am trying to simulate commodity prices using the exponential Vasicek/Ornstein-Uhlenbeck model from [Schwartz 1997][1] p. 926 Equation (1). I am using the closed form solution from [Vega 2018][2] p. 5 Equation (9) which is: $$\ln(X_{t})=\ln(X_{t-1})e^{-\theta \Delta t}+\left(\mu-\frac{\sigma^2}{2\alpha}\right)(1-e^...
I am reading a paper "A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices" cf.[A Simple Way to Estimate Bid-Ask Spreads from Daily High and Low Prices][1] [1]: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=1106193 The authors proposed the method of estimation the bid-ask spread from ...
What was the probability distribution used for Mortgage Backed Securities (MBSs) during the subprime crisis?
Under the SVJ model https://en.wikipedia.org/wiki/Stochastic_volatility_jump, what is the formula of the Black Scholes (log-normal) implied vol for an option with strike $K$ and time to maturity $T$ (assume the spot price is $1$)?
My trading returns is about 50% monthly(alpha) and maximum drawdown is about 20%. Is there a mathematical way to define the optimal withdrawal rate X%(say when profit level reach y%) to minimize risk? i.e. how to find X% & y% for the best balance between risk vs compounding rate? For e.g, withdrawing 50% of monthly pr...
I am trying to simulate commodity prices using the exponential Vasicek/Ornstein-Uhlenbeck model from [Schwartz 1997][1] p. 926 Equation (1). I am using the closed form solution from [Vega 2018][2] p. 5 Equation (9) which is: $$\ln(X_{t})=\ln(X_{t-1})e^{-\theta \Delta t}+\left(\mu-\frac{\sigma^2}{2\alpha}\right)(1-e^...
Let $\mathcal{F}$ be a $\sigma$-algebra, $P$ and $Q$ be equivalent martingale measures and $\frac{dQ}{dP}$ the Radon Nikodym Derivative. I learned that $\Bbb{E}_Q[X]=\Bbb{E}_P[\frac{dQ}{dP}X] $, which makes sense if one looks at the following: $$\Bbb{E}_Q[X]=\int_\Omega X dQ=\int_\Omega X \frac{dQ}{dP} dP=\Bbb{E}_P[...
How to price barrier options under Black-Scholes?
I'm trying to understand how a continuous double auction works, by working through the below setup: [![enter image description here][1]][1] [1]: https://i.stack.imgur.com/ZcX78.jpg I'm trying to figure out * what the final results would look like * how to determine the equilibrium price and quan...
How to find the equilibrium price in a CDA with limit orders?
I am interested in deeply understanding the way ETF market makers operate to profit. I already know that market makers profit from buying at the bid price and selling at the ask price, and I am also aware of the creation/redemption mechanism that allows them to make a profit if the ETF value deviates too much from ...
I am interested in deeply understanding the way ETF market makers operate to profit. I already know that market makers profit from buying at the bid price and selling at the ask price, and I am also aware of the creation/redemption mechanism that allows them to make a profit if the ETF value deviates too much from th...
For **market practitioners** out there: in your experience, does the below clause when ***bilateral*** is similar to a difference between `European` and `American` exercise on a vanilla option? Asking in the context of a TRS contract (either equity or fixed income). In other words, does it the presence of such cl...