Hannes Messer Case Scenario
Athena Advisors Inc. offers portfolio replication services to pension funds and insurance companies through the use of options. Clients are typically able to replicate market exposures with smaller than normal investments of funds. Athena manages exposures for its client Wertfin Insurance Company related to annuities indexed to the German Blue Chip Equity Index. Athena portfolio manager Hannes Messer is meeting with Wertfin’s risk manager, Jens Szillat, who has asked to learn more about the principles behind the option strategies being employed.
Szillat tells Messer, “I am somewhat familiar with option valuation models; however, I would like to learn more about Athena’s methodologies with respect to the index options you are managing for our portfolio.”
Messer replies, “The binomial valuation model can be applied to the two-year European style index call options we purchased one year ago. The applicable underlying instrument is the German Blue Chip Equity price index, which excludes dividends. Exhibit 1 shows the option’s characteristics at the time of purchase.”
EXHIBIT 1
BINOMIAL MODEL VARIABLES
u | 1.15 |
d | 0.90 |
π | 0.52 |
Index price | EUR 720 |
Strike price | EUR 750 |
Hedge ratio | .5697 |
1-year interest rate | 3% |
S– | 648 |
C– | 0 |
Messer explains, “Of course, with the index moving down 10% in the last 12 months, the payoffs with these options could have been replicated without using options.” Szillat responds, “My understanding is that the payoff would have been the same as the call option if you had purchased 0.5697 index units and lent EUR 356.79 at the one-year interest rate.”
Messer continues, “Twelve months ago, I noted that two-year puts with a strike price of EUR750 cost EUR38.48. Using the information in Exhibit 1 and today’s index value, the binomial valuation model calculates the current price of the put as EUR80.15. It is actually trading now above that price at EUR92.”
Szillat responds, “I am curious whether you also use the Black–Scholes–Merton (BSM) model for valuation. I understand the BSM and binomial models both have the following three assumptions in common.
Assumption 1: Trading is possible at every instant.
Assumption 2: Volatility can be predicted with certainty.
Assumption 3: The annualized returns on the underlying follow a normal distribution.
Szillat then asks, “How do you utilize the BSM model?”
Messer answers, “We use the BSM model to calculate estimates on a wide array of comparative option variables, such as how much the option value will change for a change in a particular parameter. For example, we can estimate how the rate of change of an option price speeds up or slows down for a given change in the price of the underlying index.”
Messer concludes, “We also use the BSM model to calculate the implied volatility. The implied volatilities of the index options expiring in one year are shown in Exhibit 2.”
EXHIBIT 2
IMPLIED VOLATILITY CURVE
Strike Price | Implied Volatility |
---|---|
700 | 18.71 |
710 | 17.98 |
720 | 17.38 |
730 | 16.69 |
740 | 15.83 |
750 | 15.40 |
760 | 14.50 |
770 | 14.03 |
780 | 13.21 |
790 | 12.11 |
800 | 11.09 |
Q. In describing how call option prices change, Messer is most likely referring to:
- delta.
- vega.
- gamma.
Solution
C is correct. Gamma is the change in an instrument’s delta, which is the rate at which an instrument’s price changes as the price of the underlying asset changes.
A is incorrect because delta is the option price’s rate of change for a change in the underlying.
Why is it Gamma? Change of option price is Delta. Gamma is the rate of chnage of Delta. As per the explanation given above Delta is the rate of change only
It seems you are unnecessary wasting heavy energy in pulling and putting doubts on Qforum. We have Algos that check a person’s activity level and that’s raising red flag in your name. So, I went through your doubts in the past 2 weeks and I found that your energy levels are getting unnecessarily consumed in the same. You need to restrain ………….not that it’s problematic for us to reply, but, it would hurt you, especially in these final days if you continue this mental state. So, I urge you to restrain and focus on your studies.
Infact, its surprising to see that u havent replied to anyone else doubt. So, change ur role and start answering.
Yes sir I have not replied to anyone’s doubt because I am not a subject expert for that topic. According to me if I give any wrong answer unknowingly then it will also affect that other person. In fact this happened with me in one of my previous doubts where I have raised a doubt o Residual Income but it was not explained correctly. So what’s the point in giving wrong answers?