Why do options have convexity

As the name itself implies, the trader has the option to buy the underlying in the case of a call option or sell the underlying in the case of a put option. If one buys a call option, then the implication is that the expected value of the payout is higher than the future value of the underlying.

Convexity has much to do with the interpretation of derivative pricing. Some traders, as a result of this relationship, believe portfolios should always be long gamma which means owning options.

Traders who do sell options uncovered will at points learn painfully that you can lose many multiples of your premium. Owning options is a simple way to cut off left-tail risk completely, limit drawdowns in a certain part of your portfolio, while also keeping the big upside. That said, selling volatility is certainly viable if done in a smart way. Many traders also use options not as a means to make bullish or bearish wagers, but for prudent hedging purposes.

Some also sell options as part of a core strategy , by selling options and covering that position by being long or short the underlying for a call or put option, respectively. With respect to bonds, for example, convexity is the second derivative of price with respect to interest rates.

Duration is the first derivative of price with respect to interest rates. In these cases, like with discounted cash flow price outputs while changing the required yield i. Due to convexity, they will see more price appreciation when the yield of their bond decreases from 4 percent to 2 percent than they would going from 6 percent to 4 percent.

When purchasing at ATM straddle, it is essentially a pure bet on volatility. There is no delta in the trade initially. Namely, there is no sensitivity to the option value based on the price. The delta nets out to zero. There is no position taken on the underlying security or instrument. One benefits simply from the extent of movement of the underlying and not the direction.

Some traders will choose to delta hedge a straddle when they do get price movement. With the growth of listed options and active ETFs, convexity can now be accessed through publicly available investments. Options-Based Convexity Strategies With the core goal of convexity being strong outperformance relative to a benchmark in more extreme markets, options are a natural tool for designing convex investment strategies.

Utilizing deep out-of-the money options, one can buy large amounts of equity protection on the downside and equity enhancement on the upside, creating non-linear payoffs as markets move significantly. Research Blog Thought leadership on asset allocation, practice management and markets to help advisors build impactful portfolios. Case Studies In-depth analyses providing implementable solutions to the most pressing advisory problems.

View All Case Studies. Research Tools Performance analysis and asset allocation tools to help advisors clarify their research process. This is the key to identifying convexity. Payoffs are non-linear not because the asset is volatile. Payoffs are non-linear because the delta of your position is changing. If you are dealing with an instrument whose exposure changes for the same given change, you are dealing with a non-linear exposure.

Curvature is a nice term because it reminds us that we are concerned with the shape of a payoff. Curvature indicates that the slope of your payoff changes. Your delta is morphing due to time, changes in volatility, and in these examples, due to changes in the asset price. Option deltas do change. Curvature refers to the idea that the delta of that call does not stay constant. When we zoom into the classic hockey stick graph of a call option value with respect to stock we can see the curvature.

If you drive a car 30mph for 30 minutes you will travel 15 miles. If 10 minutes into the trip you instantly accelerated to 60mph and stayed at the speed for 20 more minutes you will find that you have traveled 25 miles. The difference between 25 miles and your original linear estimate of 15 miles is curvature. In the analogy, your velocity at any one point in time is your delta. The change in velocity as you went up a gear was a change in delta and Greekophiles will recognize the acceleration as gamma.

If you want the opportunity to test your understanding go back to the call overwriter example:. Bonds have naturally curved payoffs with respect to interest rates. Consider the present value of a note with the following terms:.

It turns out then as interest rates fall, you actually make money at an increasing rate. Bonds with longer duration tend to come with higher convexity, but for the people who try to maintain the same duration, that is where derivatives or options comes in. You can either reduce convexity by selling bonds with embedded options like callable bonds, mortgage backed securities and vice versa.

For those who are eligible to buy derivatives without constraint lots of fixed-income managers are not allowed to touch derivatives , they can purchase future contracts. To give you a sense, a US 2 Year might have a duration close to 2 with an effective convexity of 0. Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more.

What does it mean to long the convexity of options? Ask Question. Asked 9 years, 5 months ago. Active 11 months ago. Viewed 30k times. Specifically, he says; The spread between the VIX sitting there at 20 for a period of time and this realized vol of only 10, that's a big spread.

Improve this question. Ellie Kesselman 3, 1 1 gold badge 19 19 silver badges 46 46 bronze badges. The Bloomberg link is broken — Dmitri Zaitsev. Bloomberg misspelled the person's name.

It's supposed to be Curnutt, not Curnett. Add a comment. Active Oldest Votes. First lets understand what convexity means: Convexity - convexity refers to non-linearities in a financial model.

So lets define Gamma: Gamma - The rate of change for delta with respect to the underlying asset's price. So the answer is: If we are long gamma convexity of an option it simply means we are betting on higher volatility in the underlying asset in your case the VIX. An example of being "long gamma" is a "long straddle" Side Note: I personally do trade the VIX and it can be very volatile, you can make or lose lots of money very quickly trading VIX options. Some resources: What does it mean to be "long gamma" in options trading?

Improve this answer. Kirill Fuchs Kirill Fuchs 6, 34 34 silver badges 64 64 bronze badges. Thanks for your detailed response! I didn't think of convexity as gamma, even though I'm familiar with it.

It makes sense then to long a delta-hedged straddle position to be long vol. Do you know what the "negative carry" refers to; is it the vol decay?

AK Sorry can you link me to where you see "negative carry"? Yea, it's the last line of the quote I referenced, "Options market makers will pay something to be long the convexity of options; they like to be long and are willing to pay away some of that negative carry.