Introduction
The CDS markets on Bitcoin and Ethereum do not exist. Not yet. But, it is just a matter of time. In this article, we are the first to map out the hypothetical properties of CDS spreads observable from the derivative markets.
To do so, we present a novel empirical benchmark for analyzing credit risk using “pseudo firms”. The assets of these “pseudo firms” are Bitcoins or Ethereum. The capital structure involves equity and a zero-coupon bond. By no-arbitrage, pseudo bonds are equivalent to Treasuries minus put options on pseudo-firm assets. The environment resembles the classic Merton model. Since the put option prices are observable for various strikes and maturity, we can analyze CDS spreads of “high” leverage and “low” leverage pseudo firms. We follow the AER article
Methodology
To understand the method, consider two firms as of March 07, 2021, when the spot price of Bitcoin was approximately $49,789. Suppose we form the first firm — named High Levered pseudo firm — by buying one bitcoin. In the firm charter, we set the liquidation date to December 30, 2022. We also finance the both debt and equity. Specifically, this High Levered firm issues a zero-coupon bond with a principal of $50,000 and maturity of December 30, 2022. On one hand, if the bitcoin value ends up below the principal of $50,000 on the maturity date, then the debt holder receives proceeds from liquidation. If the bitcoin value ends up above the principal of $50,000 on the maturity date, the debt holder receives the principal of $50,000 and the equity holder receives the residual liquidation proceeds. The setup resembles the classic Merton set up.
Contrary to High Levered firm, we also form a second firm — named Low Levered Pseudo firm — by selling a zero-coupon bond with the principal of $5,000 and and the same maturity. Note that the principal of the low levered firm is one-tenth of the high levered firm. In both firms, we fund the residual amount by equity so that the proceeds add up to buy one bitcoin.
The debt holder payoff is min(\(A_T\),\(K\)) where \(K\) is the principal and \(A_T\) is the random bitcoin price on the maturity date \(T\). Slight algebra shows that the payoff becomes \(K\) - max(\(K-A_T\),0). The present value of the payoff is equivalent to buying a risk-free bond with principal \(K\) and shorting a put option with strike \(K\). Most importantly, the put option price is observable and hence the bond price is observable. From the bond price, we back out the CDS spread.
Panel A of Figure 1 shows the time series of the two bond prices. The purple dots show the bond price of the High Levered firm; the blue dots show the bond price of the Low levered firm and the orange line shows the bitcoin spot price. With the fall in the bitcoin price around June 2021, the bond price of the high levered firm hovered around $29,000 — a haircut of 40%. But, around May 2021, the bond price of the low levered firm decreases to around $1,700 — a haircut of 65%.
Since the bond price depends on the put price, Panel B describes the time series of the implied volatility of both the pseudo firms. The implied volatility of the low levered firm is higher than the high levered firm. That is, implied volatility is consistent with the volatility smile behavior in the equity markets. But, the smile slope is notable. The implied volatility of the high levered firm around May 2021 is around 50%; the volatility for the low levered firm is above 150% for the low levered firm.
Note that as the time passes, the bond price changes not only because of the changes in bitcoin price and volatility but also because of changes in time to maturity. To combine the three variables together, we calculate the distance to default (DDF) which is the risk-neutral probability of the put option being in the money. Panel C shows the time series of the DDF for the two firms. As expected, the DDF for the high levered firm (purple dots) is higher than the DDF of the low levered firm (at least most of the time).
From the bond price and assuming the risk-free rate of zero, we calculated the CDS prices in Panel D. The CDS spreads for the low levered firm remain below 10% most of the time. But, the CDS spreads of the high levered firm remain above 20% most of the time. Note that around May, because of the volatility smile, the CDS prices of low levered firm is higher than high levered firms.
Figure 1: This figure gives the time series of CDS for both high and low levered pseudo firms
Data
The derivative markets are new relative to the spot BTC and ETH market. During the last few years, several exchanges have offered European options on bitcoin and ether against the US dollar. Many platforms that offer crypto options are regulated (or, at least semi-regulated) by financial market regulators such as the CFTC, including the CME, LedgerX, FTX and IQ Option. The Deribit exchange, which is registered in Panama, is self-regulated at the time of writing–and almost two-thirds of the trading volume on crypto options is currently on that exchange. By May 2021, the daily trading volume of bitcoin options on Deribit alone exceeded $3 billion.
But options on Deribit are different. The margining and settlement of options on Deribit takes place either on BTC or ETH — not USD. As a result, we use data from LedgerX. LedgerX describes itself as “the first federally regulated exchange and clearing house to list and clear fully collateralized, physically settled bitcoin swaps and options for the institutional market.”
The options on LedgerX expire at 4:00 p.m. every day. Note that options also trade on weekends. Our daily data begins on November 16, 2017, and ends on August 15, 2021.
We should make the data public and put it on a github page.
Summary Statistics
Table 1 shows the summary statistics. We made two assumptions so far. First, we assume that the risk-free rate is zero. This can be amended easily. Second, we calculate the CDS spread using put options. We can alternatively create CDS spreads using call options (using Put Call parity). We also filter option so that the open interest is above 100 (one Bitcoin)
Five observations are in order. First, majority of the options have an expiration of less than three months. The maximum maturity is about two years. Because of the lack of data, our study is markedly different that the corporate CDS, which predominantly depends on five-year CDS.
Second observation concerns the average CDS spread. As a whole, the mean CDS spread is around 148%. This number is astounding and is much higher than even junk bonds.
The third observation concerns moneyness which we defined as \(K / A_t\) where \(K\) is the strike price and \(A_t\) is the Bitcoin price. Since the average moneyness is 1.7, we analyze in-the-money put options.
What does the CDS versus Time to maturity look like
| Statistic | N | Mean | St. Dev. | Min | Pctl(25) | Pctl(75) | Max |
| DaysToExpiration | 8,826 | 73.323 | 102.083 | 2 | 12 | 90 | 728 |
| CDSPut | 8,826 | 1.484 | 4.546 | 0.0005 | 0.201 | 1.105 | 111.220 |
| open_interest | 8,826 | 1,416.827 | 1,678.464 | 101 | 368 | 1,821 | 18,622 |
| volume | 8,826 | 123.919 | 333.491 | 1 | 6 | 124 | 15,136 |
| Moneyness | 8,826 | 1.737 | 9.316 | 0.079 | 0.683 | 1.003 | 188.703 |
| ImpVol | 8,826 | 0.964 | 0.582 | 0.00004 | 0.665 | 1.124 | 5.000 |
| DDF | 8,826 | 0.388 | 0.273 | 0.000 | 0.161 | 0.568 | 1.000 |
Figure 2: This figure compares the mean CDS by days to expiration
Figure 2 shows a scatter plot of the mean CDS by days to expiration. The blue line shows a smoothed line calculated via a local regression. Overall, as the days to expiration increases, the mean CDS decreases. The decreasing profile contradicts AAA or A bonds which typically have upward sloping term structures. Figure 1 forms the first major result of the article. Overall, the BTC CDS term structure behaves like junk bonds
But, the level of CDS spreads is much higher than a typical junk bond. Cite some literature here.
What does the CDS versus Default Risk look like
In the finance literature, people measure credit risk by a credit rating. Obviously, this is not possible for us. Instead of a credit rating, we use Distance to Default (DDF). Using the implied volatility, we calculate the DDF which is the risk-neutral probability of the asset being lower than the spot price. Figure 3 shows the CDS mean across different measures of DDF. Note that DDF combines time to maturity, volatility and moneyness in one number — it is a better measure of credit risk. The positive relationship between CDS and DDF is reassuring.
Figure 3: This figure gives the plot of CDs versus implied vol
To understand the credit risk more, we divide the data into three categories based on DDF. We call the pseudo firms with DDF that is below the 25% percentile as low leverage firms; we call the pseudo firms with DDF above the 75% percentile as high leverage firms. We chose the cut-off points arbitrarily. Figure 4 shows the time series of the CDS for both high and low levered firms. We choose to show data after 2020 as the data prior to 2020 is spotty — the quote dates are not continuous because of the filters. Note that the difference between high levered firms and low levered firms is apparent. The mean CDS for low levered firms does not change through time — the mean is around 22%. The mean CDS of high levered firms varies substantially. The mean CDS of high levered firms is over 400% — the mean is above the scale of the plot.
Figure 4: This figure gives the time series of CDS for both high and low levered pseudo firms
Next Steps
Figure out the Implications — I am pitching it to several people and trying to answer so what. One idea would be compare the crypto loan rates versus what we found
Theory — The implied volatility is off the charts and clearly Brownian motion is not sufficient. Work out a VG model.
Stochastic Volatility — There is clear evidence of variance risk premium for crypto.
CDS of ETH — Compare ETH CDS relative to BTC CDS. In the market, there is a belief that ETH is safer than BTC. Show this.
Robustness — What does the behavior look like with going long spot and short the call (Put call parity). Incorporate risk-free rate? What about using bid ask spreads?