# METALS #16(b) – Taking Stock of the Pt-Pd-Au relationship (contd.)

## 14th December 2023

# OBSEVATIONS ON VOLATILITY

## A. Historical Volatility

### I use 3 methods (for comparison) for calculating historical volatility: (1) taking the whole series of close-to-close of log returns and calculating its standard deviation; (2) 10-day moving average of the realised volatility (variance of the log 10 returns) and (3) Garman-Klass model (which takes into account the open, high, low and closing prices (intraday movement is captured)).

#### A.1. Gold

A.1.1. Model 1 = 14.77%

A.1.2. Model 2: (a) Simple 10-year average = 5.75%; (b) High of the series = 8.27%; (c) Low of the series = 4.70%; (d) Volatility of the vols = 12.52%

A.1.3. Model 3: (a) Simple 10-year average = 0.66%; (b) High of the series = 8.15%; (c) Low of the series = 0.33%; (d) Volatility of the vols = 3.14%

#### A.2. Platinum

A.2.1. Model 1 = 26.47%

A.2.2. Model 2: (a) Simple 10-year average = 10.09%; (b) High of the series = 36.45%; (c) Low of the series = 6.70%; (d) Volatility of the vols = 25.66%

A.2.3. Model 3: (a) Simple 10-year average = 2.15%; (b) High of the series = 49.67%; (c) Low of the series = 0.78%; (d) Volatility of the vols = 10.20%

#### A.3. Palladium

A.3.1. Model 1 = 35.30%

A.3.2. Model 2: (a) Simple 10-year average = 13.11%; (b) High of the series = 57.91%; (c) Low of the series = 8.70%; (d) Volatility of the vols = 37.30%

A.3.3. Model 3: (a) Simple 10-year average = 4.10%; (b) High of the series = 108.53%; (c) Low of the series = 1.24%; (d) Volatility of the vols = 22.54%

****

1. On all 3 models Gold historical vol < Platinum historical vol < Palladium historical vol.

2. Model 3 (G-K) exhibits the highest numbers since it takes into account the intraday movements.

3. Model 1 is in my opinion the benchmark to use when comparing vs. implied volatility. Models 2 and 3 are easily influenced by very short-term spikes and noise (best to keep it simple). However, using volatility of the vols helps smooth numbers out.

# FEATURES ANALYSIS

1. I have used a several statistical models to analyse the relationship between Pt, Pd an Au, from linear to non-linear. As regards linear models… I could not find any significant correlationship between Pt, Pd and Au prices.

2. When a lag to Pt prices is introduced the correlationship is very significant. But I am wary that this is simply overfitting.

3. It appears that a non-linear model without manipulating the data results in a strong relationship between Pt, Pd and Au. (Note: this may influence the way the option strategy is structured – the coefficients suggest structure size should be 3x Pt to 1X Au to 2x Pd).

4. There is significant correlationship between the log returns of Pt,Pd and Au.

5. There is cointegration between the log returns of Pt, Pd and Au. Meaning….there is a long-term equilibrium relationship between their log returns. But does this mean there is mean reversion? That is, can we trade a return to Pt>Au>Pd? I posit that we can.

# OPTIONS STRATEGY

1. I will be using April 2025 options on Pt and Au; September 2024 Options on Pd.

2. Structure size will be 3xPt:1xAu:2xPd.

3. Platinum: purchase the April 2025 40 delta call (300 lots); sell the April 2025 25 delta put (300 lots) .

4. Gold: purchase the April 2025 25 delta put (100 lots).

5. Palladium: sell the September 36 delta call (200 lots).

# **** Details on option strike prices, premium and the various Greeks on the next post (Metals #16(c)) plus rationale on the structure selected.

## To win…proper formal attire required.

# OBSEVATIONS ON VOLATILITY (contd.)

## B. Implied Volatility (8 Dec 2023 close, at-the-money)

#### B.1. Gold

B.1.1. Front (Feb 2024) = 11.79%

B.1.2. Mid (Jan 2025) = 14.46%

B.1.3. Back (Dec 2025) = 14.55%

#### B.2. Platinum

B.2.1. Front (Feb 2024) = 21.16%

B.2.2. Mid (Jan 2025) = 22.25%

B.2.3. Back (Jan 2026) = 21.93%

#### B.3. Palladium

B.3.1. Front (Feb 2024) = 38.66%

B.3.2. Mid (Dec 2024) = 34.23%

B.3.3. Back (Dec 2025) = 33.74%

****

1. As with the observation on historical vols, Gold implied vol < Platinum implied vol < Palladium implied vol.

2. Implied Volatilities for Au, Pt and Pd are relatively similar to the Model 1 historical vols.

3. Implied Volatilities for Au, Pt an Pd are also relatively similar to Model 2(d) – volatility of the vols.

4. G-K Model is too sensitive to intraday noise to be any relevance when considering how to design our option strategy to play Pt>Au>Pd.

5. When historical volatilities are close to implied volatilities one cannot play the gamma trade (movement (long gamma) or no movement (short gamma – positive time decay)). therefore, the strategy will be based solely on direction. however, as much as possible one should look for the best strikes as well as minimising negative time decay.

## C. Implied Volatility Risk Reversals (8 Dec 2023 close, 25 delta (estimate based on market website))

#### C.1. Gold

C.1.1. Mid (Jan 2025) = 1.13% points puts over

#### C.2. Platinum

C.2.1. Mid (jan 2025) = 1.10% points calls over

#### C.3. Palladium

C.3.1. Mid (dec 2024) = 1.22% points puts over

****

1. Pd and Au RRs are all biased to the puts. Pt is biased to the calls – market signalling Pt is undervalued(?).

2. Implied vols and RRs are line with historicals and therefore any strategy should be net long vega.

3. More than understandable that Pd RRs are biased to the puts, but Au? Au has been the steady riser of recent months. Pd has seen a meltdown and the puts bias is most likely half of what it really you should be (i.e. 2% points).

4. It is worth noting once more than in general the implied volatiles of Pt, Pd and Au are in line with historical vols. Hence being long vega is the right strategy and therefore i shall be focusing the strategy structure on either the mid- or longer-term expiries. Some short options is warranted to finance a bit of the long vega position.

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