Stack Exchange Network

Stack Exchange network consists of 175 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

Hot answers tagged

3

It is on page 329 (which is the third page of the article) and represents the market price of volatility risk. I have copied below from the original article:


3

Estimated economic growth is built into the stock price. Therefore it is, albeit hidden, inside any model that takes stock price into account. One of the puzzles of pre Black-Scholes world was how to incorporate projected growth into an option price. One of Black and Scholes' (and Merton) main realizations was that they didn't need to parameterize growth (...


3

Asian options are more common in the FX market where corporate hedgers are concerned with the average exchange rate that affects regular streams of foreign denominated revenue. Bermudan exercise is most common for interest rate swaptions. They provide flexibility in choosing when to exercise for cancelling a swap without the added cost of an unnecessary ...


2

Current USDTRY is about 5.7. The jargon means this: The strike of a 2 month USD Call/ TRY put corresponding to a delta of 0.05 is 8, and it costs 0.6% of USD notional. TRY to plunge is what might be implied!


2

one of the most fundamental results states that the binomial model converges towards the Black Scholes model if the step size $\Delta t$ converges to zero. The Black Scholes model is an option pricing model where the underlying is given by $$ S_T = S_0 \cdot \exp \Bigl(\sigma W_t - \frac 12 \sigma^2 t \Bigr). $$ By choosing $$ u = \exp(\sigma \sqrt{\...


1

That is the "price of volatility risk" (see Page 329) When volatility can change the "attitude" of investors to these changes becomes important for pricing options. This like/dislike for vol increases is captured in the parameter $\lambda$. In practice vol goes up i.e. $dv$ is positive, in bad economic times, such as recessions, when $dC$ is negative. So $\...


1

There are lot of strategies. You can try for example: Active Collar strategy Calendar Option Strategies Dispersion trading Try to google more, or look for strategies on ssrn.com or arxiv.org ...


1

Your vega is off by a factor of 100. Change it to sigma = sigma + diff/vega/100. import datetime from scipy.stats import norm from math import exp, log,sqrt import quantsbin.derivativepricing as qbdp def find_vol(target_value, call_put, S, K, T, r): MAX_ITERATIONS = 200 PRECISION = 0.01 sigma = 0.5 s = {} for i in range(0, ...


1

Intuitively, if an option has 0 Vega (k=0), it has no influence on the single volatility that will correctly price the portfolio. If you have one position with a \$100 vega per vol point, and another with only $50 vega per vol point, then using a volatility that is 1 point above the implied volatility of the first position, but 2 points below the implied ...


1

That seems to be chapter 30 of A Handbook of Quantitative Finance and Risk Management 2010, Cheng-Few Lee, Alice C. Lee, John Lee ISBN: 9780387771175 (online) or 9780387771168 (print)


1

\begin{equation*} \begin{split} \mathbb{1}_{S_T > K, \max_{[0,T]} S_t < H} &\approx \frac{(S_T - (K-\varepsilon))^+ - (S_T - (K+\varepsilon))^+}{2 \varepsilon} \mathbb{1}_{\max_{[0,T]} S_t < H} \\ &= \frac{(S_T - (K-\varepsilon))^+\mathbb{1}_{\max_{[0,T]} S_t < H} - (S_T - (K+\varepsilon))^+\mathbb{1}_{\max_{[0,T]} S_t < H} }{2 \...


1

When you say the Black Scholes formula for currency options, I assume you are referring to the Garman-Kohlhagen formula described here. Note that this formula is based on the interest rate differential $r_d - r_f$, which essentially captures the forward premium. An even more explicit way to see this is to use the Black Model described here. Using this ...


1

The options month cycle means that option expirations are generally listed in a certain way. That way is that first, there are always two consecutive months. It is worth quickly mentioning that the expiration date is the friday after the 3rd wednesday of the month (don't hold me to that but I think that is correct). So a Jan cycle stock, on Jan 1, will have ...


1

This is not the typical Heston stochastic differential equation (SDE). In the original Heston paper, the SDE is defined without $\lambda$, that is $\lambda=1$ and $v(0)=v_0$ not necessarily 1. In your case you have to do the change of variable $y= \lambda^2 v$ which leads to $$dS/S = \sqrt{y}dW_S$$ $$dy = k(\lambda^2 - y) + \epsilon\lambda\sqrt{y} dW_y$$ ...


1

When you buy or sell an option you can choose what type of exposure you would like to have. In layman's terms, if you leave the Delta unhedged you are exposed to the price movements of the underlying. You would want that if you care about the direction of the underlying and have a view on whether prices go up or down based on whatever research you would have ...


1

You can find historical currency options quotes in WRDS . In WRDS, choose the option for Philadelphia Stock Exchange (PHLX) and then currency options. Make sure you have a WRDS account in order to access the data.


Only top voted, non community-wiki answers of a minimum length are eligible