instruction stringlengths 15 26.1k |
|---|
I'm dissatisfied with the usefulness of delta and would like to get your feedback on a slight tweak on it.
## Example
Consider two options for a made-up stock at \$5 with IVs around 120%.
### Option A:
- ITM call expiring in 180 days
- Purchase price: \$2.03
- Delta: 0.76
### Option B:
- ITM call expiring in 57 days... |
>Consider a two-period binomial model, with one risky asset. The are two types of options:
>
> - call option with strike price $K$, i.e., the payoff is given by $g(S_T)=(S_T-K)^{+}$
>- option with payoff given by the average of prices, i.e., $g(S_T)=(\frac12(S_0+S_T)-K)^{+}$
>
>where $X^{+}=\max\{X,0\}$.
>
>Assume that... |
I am doing this question that I couldn't find the payout ratio.
>For you, company equity beta is unknown, it has a target i.e. current debt to book equity ratio: 0.5 and target debt to market capitalization ratio: 0.1. Its debt is risk-free since the loan was granted by the government at a low rate to stimulate the ... |
When doing a regression based performance attribution I see that people normally use WLS.
So that both our independent and dependent variables are multiplied by our WLS matrix, which is a diagonal matrix that where the values on the diagonal are the square root of the companies market cap.
>X = X .* WLS
>
>y = y .* W... |
[[A]s implied volatility increases, option premiums become more expensive. As implied volatility decreases, options become less expensive. ](https://www.investopedia.com/articles/optioninvestor/08/implied-volatility.asp)
[Buying options when IV is 55 and selling when it is 30 is a sure way to lose money](https://www.t... |
What does the red phrase below mean?
>[doougle. 7 points 3 years ago](https://old.reddit.com/r/options/comments/4yobnc/cutting_losses/d6pakjx/).
>
> This is one of the "not as easy as it sounds" things about options. You always hear things like "Make money if the market goes up down or sideways" or "defined risk tra... |
While reading [How does implied volatility affect option pricing by Investopedia][1], it states the following in key takeaways
> - When options markets experience a downtrend, implied volatility generally increases.
>
> - Implied volatility falls when the options market shows an upward trend.
>
> - Higher implied vol... |
I deliberately haven't stipulated the kind of Quant job, as I'm asking in general. [This r/quant comment](https://old.reddit.com/r/quant/comments/92q5ck/the_types_of_math_i_need_to_know_to_be_a_quant/e3vjdte/) answers "what is complex analysis used for in quant finance?":
> Some pricing models, and some analysis of di... |
To wit, doesn't hedging necessarily break even or lose money? I assume the semi-strong form of the EMH, defined in Zvi Bodie, Alex Kane, Alan J. Marcus. [*Investments* (2018 11 edn)](https://www.amazon.ca/Investments-Zvi-Bodie/dp/1259277178/ref=dp_ob_title_bk). p 338.
> The **semistrong-form** hypo... |
To answer strictly: no there's no reference method for determining the number of days.
### Delving a bit deeper
Always remember **the profit from option trading does not come from the price at which you trade but from the mismatch between implied volatility and realised volatility**.
Moreover, **you can reap that pro... |
Thank you for your help everyone, and I apologise beforehand if this is a lousy or dumb question.
I am looking to read up more on Quadratic Loss & Linex Loss, and forecast optimality.
In my university text, we were told that the quadratic loss function is essentially the squared-error of the loss function, or square ... |
I use quantlib to bootstrap yield curve from deposit rate, future price and swap rate. But after I get curve, the date in curve.nodes() doesn't match the date of swap.
Here is the code:
```calc_date = ql.Date(3,4,2020)
ql.Settings.instance().evaluationDate = calc_date
calendar = ql.UnitedStates()
settlementDays = 2
... |
Let us consider a payment schedule $\mathcal{P}:=\{t_1,\dots,t_n\}$ which has a corresponding fixing schedule $\mathcal{F}:=\{t_0,\dots,t_{n-1}\}$. We have a series of co-terminal and co-initial swaps with coinciding float and fixed payment dates, accrual conventions and notionals $-$ the specific float rate does not m... |
I am very new to financial math so I am not sure how to do with this question. A friend sent me this question to practice but I am unsure how to begin. I read about call option . Can that be used for any option? Any help would be appreciated.
>Consider the following discrete time one-period market model. The savin... |
In his autobiography, The Education Of A Speculator, Victor Niederhoffer gives the following example:
"For perspective on why frequent payment of rakes on speculative trades leads to ruin, consider playing the following game with a brokerage house. Each day, you flip a coin. If it comes up heads, you win 1 dollar. if ... |
In the section 3.2.3 of the second edition of "Interest Rate Models - Theory and Practice" by Brigo and Mercurio, the forward-rate dynamics implied by the CIR model is derived as follow:
The CIR short-rate dynamics under the risk-neutral measure:
$d r(t)=k(\theta-r(t)) d t+\sigma \sqrt{r(t)} d W^Q(t)$
The forw... |
I tried a MonteCarlo simulation with 10000 iterations and it seems to confirm a probability of about 0.0033
However I wonder if we are interpreting the problem correctly, we are assuming infinite capital, perhaps we should take into account the gambling has to stop when you hit zero capital? Any other issues I may h... |
In the section 3.2.3 of the second edition of "Interest Rate Models - Theory and Practice" by Brigo and Mercurio, the forward-rate dynamics implied by the CIR model is derived as follow:
The CIR short-rate dynamics under the risk-neutral measure:
$d r(t)=k(\theta-r(t)) d t+\sigma \sqrt{r(t)} d W^Q(t)$
The forw... |
How about using the ATM option expiring closest to your futures contract delivery date? As in :
+ Stock price : price today
+ Futures price : price at a future date, usually the nearest expiring contract.
+ Option price : price ATM at a comparable future date. |
I am attempting to calculate the one-month 95th and 99th percentile profits for a two-year portfolio of energy-generating assets over the next three months. This means that the calculation has two components: 1) monthly electricity generation during the aforementioned two-year span and 2) energy futures prices (for eac... |
Whats the issue if we try to price a swaption with a negative strike using Black model? |
Consider the Black-Scholes equation for a European Call Option,
\begin{equation}
\begin{cases}\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r\frac{\partial V}{\partial S} -rV = 0, \ &\text{for} \ (S,t)\in\mathbb{R}^+\times[0,T] \\
V(S,T) = \max(S-K,0), &\text{for} \ S\i... |
May someone please explain the intuition behind the Black-Scholes Equation? |
Consider the Black-Scholes equation for a European Call Option,
\begin{equation}
\begin{cases}\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r\frac{\partial V}{\partial S} -rV = 0, \ &\text{for} \ (S,t)\in\mathbb{R}^+\times[0,T] \\
V(S,T) = \max(S-K,0), &\text{for} \ S\i... |
Consider the Black-Scholes equation for a European Call Option,
\begin{equation}
\begin{cases}\frac{\partial V}{\partial t} + \frac{1}{2}\sigma^2 S^2 \frac{\partial^2 V}{\partial S^2} + r\frac{\partial V}{\partial S} -rV = 0, \ &\text{for} \ (S,t)\in\mathbb{R}^+\times[0,T] \\
V(S,T) = \max(S-K,0), &\text{for} \ S\i... |
Could you please explain why to calculate the asset price under risk-neutral probability, we have to take the expectation of the future cashflow, while in the normal world, we don't have to take the expectation of future cashflow ? (i.e. we keep the same amount of future cashflow then discounted for its required rate o... |
> Hence how would we know the value of V(S,T)=max(S−T,0),for S∈R+?
You know the value at time T as a function of S: it is simply the pay out, which is $\max(S-K,0)$, where $K$ is a strike.
> Moreover, why do we care to solve for V(S,t),for t<T if a European
> option may only be exercised at the maturity time... |
so Implied Volatility is computed by equalizing the value of the call option given by the black and scholes model with the one observed.
Then, by inversing $C_{BS}$, one gets "$\sigma_{IMP}$". My question would be, is $\sigma_{IMP}$ a function of the time to maturity ? Or, is it as I understood, it is "annualized".... |
Implied Volatility, annualized quantity ? And Total Implied volatility |
> while in the normal world, we don't have to take the expectation of future cashflow
Grossly incorrect. The formula or approach are exactly the same: the value of an asset is the expectation of its discounted cash flow. The only difference is the discount rate. If you have a nonlinear instrument such as a vanilla E... |
In terms of the settings, we know the current stock price, we have assumed that the stock price dynamics follow Geometric Brownian motion (GBM), we know the parameters of this process (volatility etc), and we know the characteristics of the options (option type, maturity). In practice, we know the current price of the ... |
Gain-loss ratio = E[X]/E[X_];
Calmar ratio = E[X]/MDD;
Given a fixed time time horizon [0,T], with T > 0, and given two cumulative return paths X,Y (sprocesses with time index running over [0,T]) such that X(w) < Y(w) pointwise (for every outcome w in the sample space) , then it easily seen that there is n... |
Why Calmar ratio is considered not satisfy monotonicity? |
I am trying to understand the concept of spot rates better.
Does a 2-year spot rate indicate the rate you get for a two year bond or the rate you should discount the second year cash flow for an annual coupon bond?
Same for a 3-year spot rate. |
If you want to include futures spread either as a response or predictor, I would imagine you also need to include time to expiration.
What is the industry standard way to factor time into a model or to model futures spreads? Is it as simple as just including time to expiration as an additional predictor? Or do peo... |
What's the industry standard/typical way to model contango or futures spreads? |
If you want to include futures spread either as a response or predictor, I would imagine you also need to include time to expiration somewhere in your model.
What is the industry standard way to factor time into a model or to model futures spreads? Is it as simple as just including time to expiration as an addition... |
Mid price is so noisy so I try to use the weighted price, which is much better.
However I want to define a better price called weighted price
**My questions are:**
1. How can I get a good weighted price
2. How to judge the weighted-price. How can I define an indicator to judge whether the weighted price is... |
Can anyone explain to me what trading inside/ outside the spread mean?
And why are trades that occured outside the spread are to be considered anomalous?
Thanks |
I'm not sure if this question has a concrete answer or if it's more of a fun game, but I suppose the question that does have a concrete answer is what's the most difficult instrument to value that has actually been traded OTC?
For the game part of it, what is the most difficult thinkable instrument to value, and if ... |
What are the most difficult/computationally expensive/infeasible derivatives to price? |
Consider this schematic of the bid-ask spread. Now think about a trade happening somewhere on the horizontal line. When would you say it's inside or outside? How can a trade be in the outside area?
[![The spread][1]][1]
[1]: https://i.stack.imgur.com/Lpsn9.png |
Actually the recent work by Koijen and Gabaix tries to tackle precisely a similar question.
They do not have a paper yet. Here's the link: https://www.youtube.com/watch?v=apCxV8zxoOc
They find that buying 1% of the market increases prices by 5-12%. I.e. markets are inelastic. So if this is true for the market, I... |
I am working through Paul Wilmott introduces Quantitative Finance, 2nd ed. I am failing to reproduce one of his numerical examples and I would like to understand why.
I chapter 3, Wilmott introduces the binomial option pricing model. He gives a numerical example on p. 80 (section 3.17). The example is about pricing... |
How to calculate basis swap fair spread Using Quantlib 'floatfloatswap'? |
Where can I find a rigorous proof of the Dupire formula (for example, using using Gyöngy's theorem)? I imagine this would be covered by a paper or by a standard financial math text, but I could not find one. To save space, if such a reference of a rigorous derivation for the Dupire formula exists, posting the reference... |
Prompted by a question that came up the comments [here](https://quant.stackexchange.com/questions/54970/rigorous-proof-of-dupire-formula-e-g-using-gy%c3%b6ngys-theorem), namely why we can apply the Ito lemma to a function of the form $f(x)=(x-K)^{+}$, I would be interested in knowing what are the least restrictive cond... |
Prompted by a question that came up in the comments [here](https://quant.stackexchange.com/questions/54970/rigorous-proof-of-dupire-formula-e-g-using-gy%c3%b6ngys-theorem), namely why we can apply the Ito lemma to a function of the form $f(x)=(x-K)^{+}$, I would be interested in knowing what are the least restrictive c... |
$C$ is a $N\times N$ covariance matrix of stock returns. Assuming $w$ is a vector of positions in each asset, the total variance of the portfolio is
$$w^TCw$$
The contribution to total variance of the N stocks is
$$\text{contributiontoVariance} = \sqrt Cw$$
where we use the matrix square root such that $\sqrt C\sqr... |
Is there a generally accepted definition of skew for volatility smiles? Is skew always defined as
$$
\frac{\partial{\widehat{\sigma}(K,T)}}{\partial{K}},
$$
where $\hat{\sigma}:[0;+\infty)\times[0;+\infty)\to[0;+\infty)$ is the implied volatility surface ?
Is it typical to work with ATMF skew and not look at ot... |
An investor with utility curve $U(.)$ has wealth $X_t$ at time t. He invests
- A proportion $p$ of his wealth in a risky asset that follows a geometric Brownian motion, with parameters $\mu$ and $\sigma$, and the remaining proportion $1-p$ in the risk-free asset, with continuous rate r.
Q1.) How would one find t... |
Given two Brownian motions $W_t^1, W_t^2$, we can have them correlated by
$$dW_t^1 = \rho d W_t^2+\sqrt{1-\rho^2}dZ_t$$
where $W_t^{2}$ and $Z_t$ are independent of each other.
My question then: is there any similar relationship between fractional Brownian motions? In other words, given $W_t^{H_2}, Z_t^{H_3}$ two... |
How are SOFR futures contract quotes determined? |
Im currently working on constructing the risk neutral probability distribution of a stock, based on the option prices. In doing so, i calculate the implied volatilities from the option prices, and then construct densities.
I have not yet normalized the densities in the plot below.
As the expiration date increases... |
I am researching and learning about option-implied RNDs and transformation to RWDs using expected utility theory to compute risk aversion values.
This is quite a new field for me, however I am a bit aware (although not super extensively) of equity premium puzzle and ultra high risk aversion values that come from obser... |
Does equity premium puzzle affect option-implied RWDs using Arrow-Debreu equilibrium? |
Why is Calmar ratio considered not satisfy monotonicity? |
1. Let's say I have daily returns. Don't they depend on the risk per trade I am using? Obviously, if I'm risking 2% of equity per trade returns will be drastically different than when I'm using 10%? So if I have a strategy I have to assume a certain % risk per trade in order to calculate Sharpe? Wouldn't it be too eas... |
1. Let's say I have daily returns. Don't they depend on the risk per trade I am using? Obviously, if I'm risking 2% of equity per trade returns will be drastically different than when I'm using 10%? So if I have a strategy I have to assume a certain % risk per trade in order to calculate Sharpe? Wouldn't it be too eas... |
Question1: I think you're confused on what you're actually measuring. Don't think about this in terms of trades, think about it in terms of the total value of your portfolio. At day 1 you have 100 dollars, tomorrow you have 110, 2 days from now 115 and a week from now it's back to 105. How many trades you made during t... |
We have the following definitions
$\text{Gain-loss ratio} = \frac{E[X^+]}{|E[X^-]|}=\frac{E[X^+]}{-E[X^-]}=\frac{E[X]}{-E[X^-]}+1$;
where $X,X^+,X^-$ are the returns, the non-negative returns, the negative returns, respectively; so that $E[X]=E[X^+]-E[X^-].$
$\text{Calmar ratio} = \frac{E[X]}{MDD}$
where $\... |
Why is Calmar ratio considered not to satisfy monotonicity? |
We have the following definitions
$\text{Gain-loss ratio} = \frac{E[X^+]}{|E[X^-]|}=\frac{E[X^+]}{-E[X^-]}=\frac{E[X]}{-E[X^-]}+1$;
where $X$ are the returns, $E[X^+]$ is the expected gain, i.e. $E[X|X\ge 0]\times P[X\ge0]$, $E[X^-]$the expected loss i.e. $E[X|X< 0]\times P[X<0]$; and we have $E[X]=E[X^+]-E[X^-].... |
maybe an ill-posed question, please advise
What is the difference between these 3 concepts?
- money management
- asset allocation
- portfolio optimisation
They all seem about optimising some risk/reward ratio... |
maybe an ill-posed question, please advise
What is the difference between the 3 concepts? They all seem about optimising some risk/reward ratio...
- money management
- asset allocation
- portfolio optimisation
|
I am researching and learning about option-implied RNDs (risk neutral densities) and transformation to RWDs (risk world densities) using expected utility theory to compute risk aversion values.
This is quite a new field for me, however I am a bit aware (although not super extensively) of equity premium puzzle and ul... |
In the litterature we specify a dynamic for $\frac{P(T,T_{p})}{A(T)} = G(S(T))$ for each Swap rate S(T) , and there are supposed independant so that we can obtain some value using copulas for calculing the CMS spread with payoff $( S_{1}(T)-S_{2}(T) - K)_{+}$.
But in reality the swap rates are not independant so that ... |
Is there a way to get convexity adjustements for any CMS-payoffs? |
"Money management" is the art or business of managing money on behalf of an investor (individual or institutions such as pension fund, college endowment, etc.).
Money managers usually organize their work by making decisions in a hierarchical fashion on 3 different levels:
* Strategic Asset Allocation (highest le... |
Recently there was a nice question asked on convexity of American put w.r.t strike: https://quant.stackexchange.com/questions/54667/convexity-of-an-american-put-option
Does the same hold for a Bermudan option in rates, where they underlyings are different swap rates? Say you have a Bermudan callable every one year f... |
How do we compute FX volatility for any given strike, time to maturity and FX forward? |
"Money management" is the art or business of managing money on behalf of an investor (individual or institutions such as pension fund, college endowment, etc.).
Money managers usually organize their work by making decisions in a hierarchical fashion on 3 different levels:
* Strategic Asset Allocation (highest le... |
How do we compute FX volatility for any given FX strike and time to maturity? |
1. Let's say I have daily returns. Don't they depend on the risk per trade I am using? Obviously, if I'm risking 2% of equity per trade returns will be drastically different than when I'm using 10%? So if I have a strategy I have to assume a certain % risk per trade in order to calculate Sharpe? Wouldn't it be too eas... |
Question1: I think you're confused on what you're actually measuring. Don't think about this in terms of trades, think about it in terms of the total value of your portfolio. At day 1 you have 100 dollars, tomorrow you have 110, 2 days from now 115 and a week from now it's back to 105. How many trades you made during t... |
I would like to compare two strategies through the alpha Carhart obtained. The idea is to find out which one is more profitable (or the least bad). For the first strategy, I obtained a significant negative alpha. For the second one, the alpha is positive but not significant.
I would like to be sure to interpret this... |
We have the following definitions
$\text{Gain-loss ratio} = \frac{E[X^+]}{|E[X^-]|}=\frac{E[X^+]}{-E[X^-]}=\frac{E[X]}{-E[X^-]}+1$;
where $X$ are the returns, $E[X^+]$ is the expected gain, i.e. $E[X|X\ge 0]\times P[X\ge0]$, $E[X^-]$the expected loss i.e. $E[X|X< 0]\times P[X<0]$; and we have $E[X]=E[X^+]-E[X^-].... |
How is it possible for there to be trading "premarket" and "after hours"? I thought the exchange is closed and thus trading during "premarket" and "after hours" is impossible. Are such price changes "premarket" and "after hours" caused by changes in stock futures? |
I am still relatively new to asset pricing factor models and have a few questions about my current empirical study. I would be very pleased if you could help me.
I have created a new factor which I now want to integrate into existing factor models. I want to see if the new factor makes a significant contribution to ... |
How to do Fama French (1993) cross sectional regressions? A few questions |
I am still relatively new to asset pricing factor models and have a few questions about my current empirical study. I would be very pleased if you could help me.
I have created a new factor which I now want to integrate into existing factor models. I want to see if the new factor makes a significant contribution to ... |
I am still relatively new to asset pricing factor models and have a few questions about my current empirical study. I would be very pleased if you could help me.
I have created a new factor which I now want to integrate into existing factor models. I want to see if the new factor makes a significant contribution to ... |
I am still relatively new to asset pricing factor models and have a few questions about my current empirical study. I would be very pleased if you could help me.
I have created a new factor which I now want to integrate into existing factor models. I want to see if the new factor makes a significant contribution to ... |
I have some questions regarding the intuition behind shapes for the local volatility (LV) curve as seen in quite popular models. Let's say we have the following generalized stochastic-local volatility (SLV) model for modeling forward rates
$$dF(t)=\alpha(t)\sigma(F(t),t))dW_1(t)$$ $$d\alpha(t)=\nu\alpha(t)dW_2(t)$$
w... |
I am new to the area of local volatility interpolation and I am trying to make a decent implementation for calculating the local volatility surface from option prices using the basic methodology from the article "Volatility interpolation" by Andreassen, Huge combined with some later articles and results.
1. In the ... |
I'm a DIY investor that attempts to put together his market portfolio, tilted to increase factor exposure. Currently, I'm trying to do it based on the French-Fama 5-factor model.
This model contains so-called "profitability" factor, that is based on the evidence that stocks of companies with high profitability on av... |
Why exposure to the profitability factor increases investment premium? |
I am trying to compute Implied Volatilities from Heston OTM Call and OTM Put prices for short maturities ($\tau=$ 1 week). I am using the Carr & Madan representation, the little Heston trap formulation of the characteristic function, the Lord & Kahl algorithm for the optimal damping factor and the Kahl & Jäckel transfo... |
Recently I came across the following stochastic differential equation that "predicts" the value of a given stock:
\begin{equation}
dS_t = \mu S_t dt + \sigma S_tdW_t \\
S_t(0) =S_0
\end{equation}
where $S_t$ is the value of the stock, $\sigma$ is the volatility of the stock, $\mu$ is the drift coefficient, and $W_... |
What are the advantages and limitations of predicting future stock prices using stochastic differential equations? |
Recently I came across the following stochastic differential equation that "predicts" the value of a given stock:
\begin{equation}
dS_t = \mu S_t dt + \sigma S_tdW_t \\
S_t(0) =S_0
\end{equation}
where $S_t$ is the value of the stock, $\sigma$ is the volatility of the stock, $\mu$ is the drift coefficient, and $W_... |
I have 2 perspectives as to what model to use for a YCS option:
1. It is an at the expiry option, so hit the marginals, correlate them with a copula, and be done with it.
2. To hedge the vega, I will need to have both underlyings. Moreover, I might need to rebalance the hedge in the future (say rates move, I lose... |
I have 2 perspectives as to what model to use for a YCS option:
1. It is an at the expiry option, so hit the marginals, correlate them with a copula, and be done with it.
2. To hedge the vega, I will need to have both underlyings. Moreover, I might need to rebalance the hedge in the future (say rates move, I lose... |
I was reading a lot about the idea that long positions (call or put) have positive gamma, and short positions (call or put) have negative gamma. But I couldn't understand why. In "Bunds and Bund Futures" book, the author argues as: "The reason for this is that as the futures price rises the delta of a long call (or lon... |
As practice, I have been wanting to parse exchange data and try to build an order book algorithm on my own. I found some sample data from NYSE: ftp://ftp.nyse.com/Real%20Time%20Data%20Samples/NYSE%20XDP/.
I tried using tcpdump to read the pcap data. However, that does not get the underlying market data.
Does anyon... |
In finance, alternative risk measures such as value-at-risk (VaR) and GARCH are introduced as replacements to standard deviation volatility. Is there any application or value where several risk estimators or two are considered simultaneously, for example, as a ratio that describes the divergence between one another? Or... |
As a coincidence I have also started to learn about and implement stochastic vol models.
So I first want to say that I am no expert in the field.
However, I just struggled through implementations of calibration and simulation of the Heston model.
For the calibration I used the article "Full and fast calibration of ... |
As a coincidence I have also started to learn about and implement stochastic vol models.
So I first want to say that I am no expert in the field.
However, I just struggled through implementations of calibration and simulation of the Heston model.
For the calibration I used the article "Full and fast calibration of ... |
As a coincidence I have also started to learn about and implement stochastic vol models.
So I first want to say that I am no expert in the field.
However, I just struggled through implementations of calibration and simulation of the Heston model.
For the calibration I used the article "Full and fast calibration of ... |
As a coincidence I have also started to learn about and implement stochastic vol models.
So I first want to say that I am no expert in the field.
However, I just struggled through implementations of calibration and simulation of the Heston model.
For the calibration I used the article "Full and fast calibration of ... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.